Vol. 11, No. 3, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12, 1 issue

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Dimension-free $L^p$ estimates for vectors of Riesz transforms associated with orthogonal expansions

Błażej Wróbel

Vol. 11 (2018), No. 3, 745–773
Abstract

An explicit Bellman function is used to prove a bilinear embedding theorem for operators associated with general multidimensional orthogonal expansions on product spaces. This is then applied to obtain Lp boundedness, 1 < p < , of appropriate vectorial Riesz transforms, in particular in the case of Jacobi polynomials. Our estimates for the Lp norms of these Riesz transforms are both dimension-free and linear in max(p,p(p 1)). The approach we present allows us to avoid the use of both differential forms and general spectral multipliers.

Keywords
Riesz transform, Bellman function, orthogonal expansion
Mathematical Subject Classification 2010
Primary: 42C10, 42A50, 33C50
Milestones
Received: 23 January 2017
Revised: 31 July 2017
Accepted: 23 September 2017
Published: 22 November 2017
Authors
Błażej Wróbel
Mathematical Institute
Universität Bonn
Bonn
Germany
Instytut Matematyczny
Uniwersytet Wrocławski
Wrocław
Poland