# Reverse Carleson measures on the weighted Bergman spaces with invariant weight

Reverse Carleson measures on the weighted Bergman spaces with invariant weight We study the dominating sets and reverse Carleson measures on weighted Bergman spaces Aωp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A^p_\omega$$\end{document} with invariant weights in the spirit of Lueckings results from 1981 and 1985. Then, we characterize integrating derivatives of Aωp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A^p_\omega$$\end{document} functions, and combine this with reverse Carleson measures to characterize the reverse Carleson inequality for the derivatives of Aωp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A^p_\omega$$\end{document} functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Functional Analysis Springer Journals

# Reverse Carleson measures on the weighted Bergman spaces with invariant weight

, Volume 12 (4) – Oct 1, 2021
28 pages      /lp/springer-journals/reverse-carleson-measures-on-the-weighted-bergman-spaces-with-jemMKx0lyX
Publisher
Springer Journals
ISSN
2639-7390
eISSN
2008-8752
DOI
10.1007/s43034-021-00139-4
Publisher site
See Article on Publisher Site

### Abstract

We study the dominating sets and reverse Carleson measures on weighted Bergman spaces Aωp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A^p_\omega$$\end{document} with invariant weights in the spirit of Lueckings results from 1981 and 1985. Then, we characterize integrating derivatives of Aωp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A^p_\omega$$\end{document} functions, and combine this with reverse Carleson measures to characterize the reverse Carleson inequality for the derivatives of Aωp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A^p_\omega$$\end{document} functions.

### Journal

Annals of Functional AnalysisSpringer Journals

Published: Oct 1, 2021

Keywords: Weighted Bergman space; Invariant weight; Dominating set; Reverse Carleson measure; 42B35; 32A36