Da Lio-Rivi\`{e}re-Wettstein-type inequality for weighted Bergman spaces

TL;DR

This paper extends the Da Lio-Rivi extbackslash{}`{e}re-Wettstein inequality to weighted Bergman spaces, providing boundary-value characterizations and new results on the upper plane that are not directly derived from disk cases.

Contribution

It introduces a weighted Da Lio-Rivi extbackslash{}`{e}re-Wettstein inequality and explores boundary-value characterizations for weighted Bergman spaces, including novel results on the upper plane.

Findings

Established a weighted Da Lio-Rivi extbackslash{}`{e}}re-Wettstein inequality.

Provided boundary-value characterizations of weighted Bergman spaces.

Derived results on the upper plane not directly linked to disk cases.

Abstract

In this paper, inspired by the work of Da Lio-Rivi\`{e}re-Wettstein, we investigate the boundary-value characterizations of weighted Bergman spaces and establish a weighted Da Lio-Rivi\`{e}re-Wettstein inequality. In addition, we obtain analogous results on the upper plane which does not seem to be a direct consequence of the ones on the unit disk.