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weighted COMPOSITION OPERATORS ON weighted dirichlet spaceS

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Acta Mathematica Scientia 2013年第4期33卷 1119-1126页

作者：刘小松娄增建 Department of Mathematics Shantou University

We characterize the boundedness and compactness of weighted composition operators on weighted dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.

关键词： weighted composition operator weighted dirichlet space s-Carleson mea-sure Nevanlinna counting function

MULTIPLICATION OPERATORS ON weighted dirichlet spaceS

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Acta Mathematica Scientia 2024年第6期44卷 2225-2248页

作者： Kaikai HAN Yucheng LI Maofa WANG School of Statistics and Mathematics Hebei University of Economics and BusinessShijiazhuang 050061China School of Mathematical Sciences Hebei Normal UniversityShijiazhuang 050024China School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

In this paper,we study multiplication operators on weighted dirichlet spaces D_(β)(β∈R).Let n be a positive integer and β∈R,we show that the multiplication operator M_(z)^(n) on D_(β) is similar to the operator ⊕_(1)^(n)M_(z)on the space⊕_(1)^(n)D_(β).Moreover,we prove that M_(z)^(n)(≥2)on Dβis unitarily equivalent to ⊕_(1)^(n)M_(z) on⊕_(1)^(n)D_(β) if and only if β=*** addition,we completely characterize the unitary equivalence of the restrictions of M_(z)^(n) to different invariant subspaces z^(k)D_(β)(k≥1),and the unitary equivalence of the restrictions of M_(z)^(n) to different invariant subspaces S_(j)(0≤jspaces A_(α)^(2)(α∈R)on D(in fact,the family of spaces A_(α)^(2)(α∈R)is the same with the family of spaces D_(β)(β∈R))in terms of the multiplier algebra of the underlying function *** this paper,we give a new characterization of the commutant A′( M_(z)^(n))of M_(z)^(n)on D_(β),and characterize the self-adjoint operators and unitary operators in A'(M_(z)^(n)).We find that the class of self-adjoint operators(unitary operators)in A'(M_(z)^(n))when β≠0 is different from the class of self-adjoint operators(unitary operators)in A′( M_(z)^(n))when β=0.

关键词： multiplication operator weighted dirichlet space similarity unitary equivalence commutant

Reducing Subspaces for ■ on weighted Hardy space over Bidisk

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Journal of Mathematical Research with Applications 2021年第5期41卷 510-530页

作者： Bian REN Yanyue SHI School of Mathematic Sciences Ocean University of China

In this paper, we characterize the reducing subspaces for Toeplitz operator ■, where ■ are the multiplication operators on weighted Hardy space H~2(D~2),k=(k, k), l=(l, l), k≠l and k, lare positive integers for i=1, 2. It is proved that the reducing subspace for T generated by z~m is minimal under proper assumptions onω. The Bergman space and weighted dirichlet spaces D(D~2)(δ> 0) are weighted Hardy spaces which satisfy these assumptions. As an application, we describe the reducing subspaces for ■ on D(D~2)(δ> 0), which generalized the results on Bergman space over bidisk.

关键词： reducing subspaces weighted dirichlet space commutant algebra

Generalized Cesàro Operator on dirichlet spaces

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Journal of Mathematical Research and Exposition 2006年第2期26卷 207-212页

作者：唐笑敏湖州师范学院理学院

In this paper, we study the boundedness of the generalized Cesàro operator on the weighted dirichlet spaces Dα={f∈H（D）;‖f‖Dα^2=｜f（0）｜^2＋∫D｜f＇（z）｜^2（1-｜z｜^αdm（z）〈＋∞},where -1 〈 α 〈＋∞ an... 详细信息

关键词： weighted dirichlet space generalized Cesàro operator weighted compositiono perator boundedness.