Weighted composition operators between spaces of Dirichlet type

Abstract

In this work we characterize boundedness and compactness of weighted composition operators acting between Dirichlet type spaces by using Carleson measures. We also find essential norm estimates for these operators.

Compact Weighted Composition Operators Between -Spaces

“…Operator-theoretic properties of weighted composition operators from L p (µ) into itself were studied in [1,8,9] and such operators acting between distinct L p -spaces in [3][4][5]. However, some results and proofs in [5] are rather sketchy or incomplete. In this paper, we completely characterise compact weighted composition operators between L p -spaces and illustrate the results with examples.…”

Order boundedness of weighted composition operators on weighted Dirichlet spaces and derivative Hardy spaces

“…However, for the case of p ≥ q, the corresponding characterizations were partly investigated in [9,25], where several questions were still open. Base on their works and inspired by the ideas from [2], Kumar [15] obtained the characterizations for the boundedness and compactness of weighted composition operators W φ,ϕ between different weighted Dirichlet spaces.…”

Basic properties of multiplication and composition operators between distinct Orlicz spaces

“…They also play an important role in the study of operators on Hilbert spaces. Consequently, by now there exists a vast literature on the properties of these transformations in various function spaces; we refer the interested reader to the beautiful books [5,35,36], and, for more recent studies, to [9][10][11]14,23,25], for instance.…”