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Embeddings of generalised Morrey smoothness spaces

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Acta Mathematica Sinica,English Series 2024年

作者： Dorothee D.HAROSKE Zhen LIU Susana D.MOURA leszek skrzypczak Institute of Mathematics Friedrich Schiller University Jena Faculty of Mathematics & Computer Science Adam Mickiewicz University ul.Uniwersytetu Poznańskiego 4 University of Coimbra Department of MathematicsCMUC

We study embeddings between generalised Triebel-Lizorkin-Morrey spaces εφ,p,qs(Rd) and within the scales of further generalised Morrey smoothness spaces like Nφ,p,qs(Rd),Bp,qs,φ(Rd) and Fp,qs,φ(Rd).The latter have been investigated in a recent paper by the first two authors(2023),while the embeddings of the scale Nφ,p,qs(Rd) were mainly obtained in a paper of the first and last two authors(2022).Now we concentrate on the characterisation of the spaces εφ,p,qs(Rd).Our approach requires a wavelet characterisation of those spaces which we establish for the system of Daubechies’ *** we prove necessary and sufficient conditions for the embedding εφ1,p1,q1s1(Rd)→εφ2,p2,q2s2(Rd).We can also provide some almost final answer to the question when εφ,p,qs(Rd) is embedded into C(Rd),complementing our recent findings in case of Nφ,p,qs(Rd).

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Continuous Embeddings of Besov-Morrey Function Spaces

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Acta Mathematica Sinica,English Series 2012年第7期28卷 1307-1328页

作者： Dorothee D. HAROSKE leszek skrzypczak Mathematical Institute Friedrich-Schiller-University Jena Faculty of Mathematics and Computer Science Adam Mickiewicz University

We study embeddings of spaces of Besov-Morrey type, MB p1^s1 q1^r1（R^d）→MB p2^s2 q2^r2（R^d） and obtain necessary and sufficient conditions for this. Moreover, we can also charaeterise the special weighted situation Bp1^s1 （R^d ,w）→MB p2^s2 q2^r2（R^d） for a Muekenhoupt A∞ weight w, with wα（x） = ｜x｜^a, 〉 -d, as a typical example.

关键词： Weighted Besov spaces Besov Morrey spaces continuous embeddings

Complex Interpolation of Weighted Besov and Lizorkin–Triebel Spaces

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Acta Mathematica Sinica,English Series 2014年第8期30卷 1297-1323页

作者： Winfried SICKEL leszek skrzypczak Jan VYBíRAL Friedrich-Schiller-Universitt Jena Mathematisches InstitutErnst-Abbe-Platz 207743 JenaGermany Adam Mickiewicz University Poznan Faculty of Mathematics and Computer ScienceUl.Umultowska 8761-614 PoznańPoland Technical University Berlin Department of MathematicsSecretary office MA 4-1Street of 17.June 13610623 BerlinGermany

We study complex interpolation of weighted Besov and Lizorkin–Triebel *** used weights w0,w1 are local Muckenhoupt weights in the sense of *** a first step we calculate the Calder′on products of associated sequence ***,as a corollary of these investigations,we obtain results on complex interpolation of radial subspaces of Besov and Lizorkin–Triebel spaces on Rd.

关键词： Muckenhoupt weights local Muckenhoupt weights weighted Besov and Lizorkin-Triebel spaces radial subspaces of Besov and Lizorkin-Triebel spaces complex interpolation Calderon products

Unboundedness properties of smoothness Morrey spaces of regular distributions on domains

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Science China Mathematics 2017年第12期60卷 2349-2376页

作者： HAROSKE Dorothee D. MOURA Susana D. SCHNEIDER Cornelia skrzypczak leszek Institute of Mathematics Friedrich Schiller University Jena CMUC Department of Mathematics University of Coimbra Mathematics Department Friedrich-Alexander University Erlangen-Nremberg Faculty of Mathematics and Computer Science Adam Mickiewicz University

We study unboundedness of smoothness Morrey spaces on bounded domains ? ? R^n in terms of growth envelopes. It turns out that in this situation the growth envelope function is finite—in contrast to the results obtained by Haroske et al.(2016) for corresponding spaces defined on R^n. A similar effect was already observed by Haroske et al.(2017), where classical Morrey spaces M_(u,p)(?) were investigated. We deal with all cases where the concept is reasonable and also include the tricky limiting cases. Our results can be reformulated in terms of optimal embeddings into the scale of Lorentz spaces L_(p,q)(?).

关键词： Morrey spaces Besov spaces Triebel-Lizorkin spaces growth envelopes atomic decompositions inequalities

Happy together？ Avoidance of conspecifics by gregarious mussels

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Current Zoology 2018年第1期64卷 53-61页

作者： Anna DZIERZYNSKA-BIALONCZYK Aleksandra skrzypczak Jaroslaw KOBAK Faculty of Biology and Environmental Protection Department of Invertebrate Zoology Nicolaus CopernicusUniversity Lwowska 1 Torun 87-100 Poland

Zebra mussel is a Ponto-Caspian species invasive in Europe and North America, with great environmental impact. It lives byssally attached to hard substrata in large aggregations, which is often explained by its preferences for conspecifics, though direct evidence for such preferences has been rather limited so far. We studied the reactions of zebra mussels to conspecifics, hypothesizing that they may either be attracted to one another or form aggregations only in the absence of alternative attachment sites. In Experiment 1, we tested mussel tendency to detach from existing druses depending on druse size (2-25 individuals) and substratum type (soft: sand; hard: glass). Mussels detached significantly more often on the hard substratum and from larger druses compared to soft substratum and smaller druses, respectively. This indicates that mussels tended to avoid conspecifics at high density, particularly when alternative substratum was available. In Experiment 2, we tested the responses of single mussels to distant (3 or 15 cm) conspecifics (0, 3, 15 individuals per 2.5 l tank) on the sandy substratum. The presence of conspecifics, regardless of their distance and density, resulted in single unattached mussels staying more often in their initial positions. Mussels did not move preferentially towards or away from the conspecifics. Thus, even on unsuitable substratum mussels were not attracted by conspecifics and probably exhibited an avoidance reaction by reducing their movement. This suggests that dense mussel aggregations are formed due to the lack of available alternative attachment sites rather than due to their preferences for conspecifics.

关键词：回避反应贻贝基础类型群居环境影响高密度晶簇北美洲

8-Hydroxyquinolylnitrones as multifunctional ligands for the therapy of neurodegenerative diseases

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Acta Pharmaceutica Sinica B 2023年第5期13卷 2152-2175页

作者： Damijan Knez Daniel Diez-Iriepa Mourad Chioua Andrea Gottinger Milica Denic Fabien Chantegreil Florian Nachon Xavier Brazzolotto Anna skrzypczak-Wiercioch Ane Meden Anja Pilar Janko Kos Simon akelj Jure Stojan Kinga Saat Julia Serrano Ana Patricia Fernández Aitana Sánchez-García Ricardo Martínez-Murillo Claudia Binda Francisco López-Muoz Stanislav Gobec JoséMarco-Contelles University of Ljubljana Faculty of PharmacyLjubljana 1000Slovenia Laboratory of Medicinal Chemistry(Institute of Organic Chemistry CSIC)Madrid 28006Spain Departamento de Química Orgánicay Química Inorgánica Alcaláde HenaresMadrid 28871Spain Department of Biology and Biotechnology University of PaviaPavia 27100Italy Département de Toxicologie et Risques Chimiques Institut de Recherche Biomédicale des ArméesParis 91220France Department of Animal Anatomy and Preclinical Sciences University Centre of Veterinary Medicine JU-UAUniversity of Agriculture in KrakowKrakow 30-059Poland Institute of Biochemistry Faculty of MedicineUniversity of LjubljanaLjubljana 1000Slovenia Department of Pharmacodynamics Chair of PharmacodynamicsFaculty of PharmacyJagiellonian University Medical CollegeKrakow 30-688Poland Department of Translational Neurobiology Neurovascular Research GroupCajal Institute(CSIC)Madrid 28002Spain Biotechnology and Vegetal Biology Department Escuela Técnica Superior de Ingeniería AgronómicaAlimentaria y de BiosistemasUniversidad Politécnica de MadridMadrid 28040Spain Faculty of Health Camilo JoséCela University of Madrid(UCJC)Neuropsychopharmacology Unit“Hospital 12 de Octubre”Research InstituteMadrid 28692Spain

We describe the development of quinolylnitrones(QNs)as multifunctional ligands inhibiting cholinesterases(ChEs:acetylcholinesterase and butyrylcholinesterase—h BChE)and monoamine oxidases(hMAO-A/B)for the therapy of neurodegenerative *** identified QN 19,a simple,low molecular weight nitrone,that is readily synthesized from commercially available *** 19 has no typical pharmacophoric element to suggest ChE or MAO inhibition,yet unexpectedly showed potent inhibition of h BChE(IC50=1.06±0.31 nmol/L)and h MAO-B(IC_(50)=4.46±0.18μmol/L).The crystal structures of 19 with hBChE and hMAO-B provided the structural basis for potent binding,which was further studied by enzyme *** 19 acted as a free radical scavenger and biometal chelator,crossed the blood—brain barrier,was not cytotoxic,and showed neuroprotective properties in a 6-hydroxydopamine cell model of Parkinson's *** addition,in vivo studies showed the anti-amnesic effect of 19 in the scopolamine-induced mouse model of AD without adverse effects on motoric function and ***,chronic treatment of double transgenic APPswe-PS1δE9 mice with 19 reduced amyloid plaque load in the hippocampus and cortex of female mice,underscoring the disease-modifying effect of QN 19.

关键词： Quinolylnitrone Butyrylcholinesterase Monoamine oxidase B Alzheimer's disease Multifunctional ligands 6-Hydroxydopamine model Passive avoidance task Novel object recognition

最小子宫内膜异位症患者腹水中细胞因子及sICAM-1:寻找不孕和(或)子宫内膜异位症的识别因子

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世界核心医学期刊文摘（妇产科学分册） 2006年第2期2卷 12-13页

作者： skrzypczak J. Szczepańska M. Puk E. M. Kurpisz 朱晓明 Unit of Reproductive Biology Institute of Human Genetics Pol. Acad. Sci. ul.Strzeszyńska 32 60-479 PoznańPoland

Objective: To evaluate cytokine levels (IL-1β,TNF-α,IL-6, IL-8), soluble intercellular adhesion molecule-1 (sICAM-1)-and number of macrophages in peritoneal fluid (PF)of women with no minimal endometriosis and associated (or not) infertility in order to discriminate between infertility and/or endometriosis. Study design: Cytokines and sICAM-1 were measured by using quantitative enzyme-linked immunosorbent assay (ELISA) while the macrophages were identified by May-Grunwald-Giemsa and non-specific esterase staining and presented as medians. The measurements were performed in 78 women belonging to four selected subgroups according to their endometriosis and/or infertility status. Statistical analysis was performed using Kruskal-Wallis non-parametric ANOVA test. Additionally, discriminant function analyses were performed. Results: We have found the most elevated macrophage numbers in the groups of women with endometriosis. IL-1βdid not present any statistically significant values differentiating the analysed subgroups. IL-6 (110.0 pg/ml) and TNF-αexhibited the highest concentrations (statistically significant) in a group of fertile women with endometriosis. IL-8 clearly differentiated between the subgroups with infertility and sICAM-1 was statistically significantly elevated in the subgroups of infertile women. In the forward discriminant analysis, when subdividing the studied population according to its infertility status (we considered macrophages, IL-8 and IL-6 in order of probability values), we have found striking probability value of 92%for the correct classification into an infertile population. Conclusion: Out of the range of the analysed factors we have found only the sICAM-1 to be singled out between the standard discriminant analysis and the forward one. However, this important flagging molecule might be of considerable value for discrimination between different types of pathology at the level of immune effector function. The increased levels of TNF-αand IL-6

关键词：子宫内膜异位症 sICAM-1 细胞因子非子宫内膜异位巨噬细胞不孕妇女 allis 函数分析