• Title/Summary/Keyword: weighted Toeplitz operators

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kth-ORDER ESSENTIALLY SLANT WEIGHTED TOEPLITZ OPERATORS

  • Gupta, Anuradha;Singh, Shivam Kumar
    • Communications of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1229-1243
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    • 2019
  • The notion of $k^{th}$-order essentially slant weighted Toeplitz operator on the weighted Lebesgue space $L^2({\beta})$ is introduced and its algebraic properties are investigated. In addition, the compression of $k^{th}$-order essentially slant weighted Toeplitz operators on the weighted Hardy space $H^2({\beta})$ is also studied.

BOUNDEDNESS AND COMPACTNESS OF SOME TOEPLITZ OPERATORS

  • Kang, Si Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.3
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    • pp.467-475
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    • 2013
  • We consider the problem to determine when a Toeplitz operator is bounded on weighted Bergman spaces. We introduce some set CG of symbols and we prove that Toeplitz operators induced by elements of CG are bounded and characterize when Toeplitz operators are compact and show that each element of CG is related with a Carleson measure.

COMMUTATIVITY AND HYPONORMALITY OF TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACE

  • Lu, Yufeng;Liu, Chaomei
    • Journal of the Korean Mathematical Society
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    • v.46 no.3
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    • pp.621-642
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    • 2009
  • In this paper we give necessary and sufficient conditions that two Toeplitz operators with monomial symbols acting on the weighted Bergman space commute. We also present necessary and sufficient conditions for the hyponormality of Toeplitz operators with some special symbols on the weighted Bergman space. All the results are stated in terms of the Mellin transform of the symbol.

TOEPLITZ OPERATORS ON WEIGHTED ANALYTIC BERGMAN SPACES OF THE HALF-PLANE

  • Kang, Si-Ho;Kim, Ja-Young
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.437-450
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    • 2000
  • On the setting of the half-plane H={x+iy$\mid$y>0} of the complex plane, we study some properties of weighted Bergman spaces and their duality. We also obtain some characterizations of compact Toeplitz operators.

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TOEPLITZ OPERATORS ON BLOCH-TYPE SPACES AND A GENERALIZATION OF BLOCH-TYPE SPACES

  • Kang, Si Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.3
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    • pp.439-454
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    • 2014
  • We deal with the boundedness of the n-th derivatives of Bloch-type functions and Toeplitz operators and give a relationship between Bloch-type spaces and ranges of Toeplitz operators. Also we prove that the vanishing property of ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}}$ on the boundary of $\mathbb{D}$ implies the compactness of Toeplitz operators and introduce a generalization of Bloch-type spaces.