loading page

GENERALIZED INTEGRAL TYPE HILBERT OPERATOR ACTING BETWEEN WEIGHTED BLOCH SPACE
  • PENGCHENG TANG,
  • XUEJUN ZHANG
PENGCHENG TANG
Hunan Normal University College of Mathematics and Statistics

Corresponding Author:www.tang-tpc.com@foxmail.com

Author Profile
XUEJUN ZHANG
Hunan Normal University College of Mathematics and Statistics
Author Profile

Abstract

Let µ be a finite Borel measure on [0 ,1). In this paper, we consider the generalized integral type Hilbert operator I µ α + 1 ( f ) ( z ) = ∫ 0 1 f ( t ) ( 1 − tz ) α + 1 d µ ( t ) ( α > − 1 ) . The operator I µ 1 has been extensively studied recently. The aim of this paper is to study the boundedness(resp. compactness) of I µ α + 1 acting from the normal weight Bloch space into another of the same kind. As consequences of our study, we get completely results for the boundedness of I µ α + 1 acting between Bloch type spaces, logarithmic Bloch spaces among others.
23 Feb 2023Submitted to Mathematical Methods in the Applied Sciences
23 Feb 2023Submission Checks Completed
23 Feb 2023Assigned to Editor
28 Feb 2023Review(s) Completed, Editorial Evaluation Pending
01 Apr 2023Reviewer(s) Assigned
24 May 2023Editorial Decision: Revise Major
06 Jul 20231st Revision Received
06 Jul 2023Submission Checks Completed
06 Jul 2023Assigned to Editor
06 Jul 2023Review(s) Completed, Editorial Evaluation Pending
06 Jul 2023Reviewer(s) Assigned
07 Jul 2023Editorial Decision: Accept