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t1 theorem FOR BESOV SPACES ON NONHOMOGENEOUS SPACES

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Analysis in theory and Applications 2005年第3期21卷 280-293页

作者： Donggao Deng Yanchang Han Department of Mathematics Zhongshan University Guangzhou 510275 P. R. China Department of mathematics South China Normal University Guangzhou 510631 P. R. China

Suppose μ is a Radon measure on R^d, which may be non doubling. the only condition assumed on μ is a growth condition, namely, there is a constant Co 〉 0 such that for all x ∈ supp（μ） and r 〉 0, μ（B（x, r）） ≤ Cor^n, where 0 〈 n ≤ d. We prove t1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known tolsa＇s results. We also prove t1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7] .

关键词： Besov space t1 theorem nonhomogeneous space Calderón-Zygmund operator Littlewood-Paley theory

New Characterizations of Inhomogeneous Besovand triebel-Lizorkin Spaces over Spaces of Homogeneous type

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Acta Mathematica Sinica,English Series 2009年第11期25卷 1787-1804页

作者： Yan Chang HAN School of Mathematical Sciences South China Normal University Guangzhou 510631 P. R. China

In this paper we use the t1 theorem to prove a new characterization with minimum regularity and cancellation conditions for inhomogeneous Besov and triebel-Lizorkin spaces over spaces of homogeneous type. these result... 详细信息

关键词： t1 theorem inhomogeneous Besov and triebel-Lizorkin spaces discrete Calderon repro-ducing formula inhomogeneous Plancherel-Polya inequalities

Boundedness of a class of super singular integral operators and the associated commutators

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Science China Mathematics 2004年第6期47卷 842-853页

作者： CHEN Qionglei & ZHANG Zhifei Department of Mathematics, Zhejiang University, Hangzhou 310028, China Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China 1. Department of Mathematics Zhejiang University 310028 Hangzhou China 2. Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China

In this paper we give the (L p α, L p ) boundedness of the maximal operator of a class of super singular integrals defined by $$t_{\Omega ,\alpha }^* f(x) = \mathop {\sup }\limits_{\varepsilon > 0} \left| {\int_{|x - y| > \varepsilon } {b(|y|)} \Omega (y)|y|^{ - n - \alpha } f(x - y)dy} \right|,$$ which improves and extends the known result. Moreover, by applying an off-Diagonal t1 theorem, we also obtain the (L p , L q ) boundedness of the commutator defined by $$C_{\Omega ,\alpha } f(x) = p.v. \int_{\mathbb{R}^n } {(A(x)} - A(y))\Omega (x - y)|x - y|^{ - n - \alpha } f(y)dy.$$

关键词： singular integral operator maximal operator commutator t1 theorem