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# Title: Analysis in the multi-dimensional ball

Abstract: We study the heat semigroup maximal operator associated with a well-known orthonormal system in the d-dimensional ball. The corresponding heat kernel is shown to satisfy Gaussian bounds. As a consequence, we can prove weighted $L^p$ estimates, as well as some weighted inequalities in mixed norm spaces, for this maximal operator.
 Comments: 18 pages Subjects: Classical Analysis and ODEs (math.CA) MSC classes: 42B25 (Primary) 42C05, 31C25 (Secondary) Cite as: arXiv:1803.06195 [math.CA] (or arXiv:1803.06195v1 [math.CA] for this version)

## Submission history

From: Tomasz Zachary Szarek [view email]
[v1] Fri, 16 Mar 2018 12:42:58 GMT (20kb)