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On essential norms of singular integral operators with constant coefficients and of the backward shift
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Orientador(es)
Resumo(s)
Let X be a rearrangement-invariant Banach function space on the unit circle T and let H[X] be the abstract Hardy space built upon X. We prove that if the Cauchy singular integral operator (Formula presented) is τ−t bounded on the space X, then the norm, the essential norm, and the Hausdorff measure of non-compactness of the operator aI + bH with a, b ∈ C, acting on the space X, coincide. We also show that similar equalities hold for the backward shift operator (Formula presented) on the abstract Hardy space H[X]. Our results extend those by Krupnik and Polonskiĭ [Funkcional. Anal. i Priložen. 9 (1975), pp. 73-74] for the operator aI + bH and by the second author [J. Funct. Anal. 280 (2021), p. 11] for the operator S.
Descrição
Received by the editors November 5, 2021. 2020 Mathematics Subject Classification. Primary 45E05, 46E30, 47B38. Key words and phrases. Rearrangement-invariant Banach function space, abstract Hardy singular integral operator, backward shift operator, norm, essential norm, measure of non-compactness.
Publisher Copyright:
© 2022 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0).
Palavras-chave
abstract Hardy singular integral operator backward shift operator essential norm measure of noncompactness norm Rearrangement-invariant Banach function space Algebra and Number Theory Analysis Discrete Mathematics and Combinatorics Geometry and Topology