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Topological Structure of the Space of Weighted Composition Operators Between Different Hardy Spaces

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Abstract

We consider properties related to weighted composition operators boundedly acting from the classical Hardy space H p to H q for \({1 \leq q < p < \infty}\). Especially, we shall completely determine path connected components in the set of weighted composition operators and explicitly characterize by function-theoretic properties of analytic self-maps.

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Authors and Affiliations

  1. Department of Mathematics, Niigata University, Niigata, 950-2181, Japan

    Kei Ji Izuchi

  2. Nippon Institute of Technology, Miyashiro, Minami-Saitama, 345-8501, Japan

    Shûichi Ohno

Authors
  1. Kei Ji Izuchi
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  2. Shûichi Ohno
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Correspondence to Shûichi Ohno.

Additional information

The first author is partially supported by Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science (No.24540164).

The second author is partially supported by Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science (No.24540190).

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Izuchi, K.J., Ohno, S. Topological Structure of the Space of Weighted Composition Operators Between Different Hardy Spaces. Integr. Equ. Oper. Theory 80, 153–164 (2014). https://doi.org/10.1007/s00020-014-2142-0

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  • DOI: https://doi.org/10.1007/s00020-014-2142-0

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