Mathematical Research Letters

Volume 25 (2018)

Number 5

Bilinear spherical maximal function

Pages: 1369 – 1388

DOI: https://dx.doi.org/10.4310/MRL.2018.v25.n5.a1

Authors

J. A. Barrionuevo (Department of Pure and Applied Mathematics, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil)

Loukas Grafakos (Department of Mathematics, University of Missouri, Columbia, Mo., U.S.A.)

Danqing He (Department of Mathematics, Sun Yat-sen University, Guangzhou, China)

Petr Honzík (MFF UK, Charles University, Prague, Czech Republic)

Lucas Oliveira (Department of Pure and Applied Mathematics, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil)

Abstract

We obtain boundedness for the bilinear spherical maximal function in a range of exponents that includes the Banach triangle and a range of $L^p$ with $p \lt 1$. We also obtain counter-examples that are asymptotically optimal with our positive results on certain indices as the dimension tends to infinity.

The second author acknowledges the support of Simons Foundation and of the University of Missouri Research Board and Research Council.

The third author was supported by NNSF of China (No. 11701583), Guangdong Natural Science Foundation (No. 2017A030310054) and by the Fundamental Research Funds for the Central Universities (No. 17lgpy11).

The fourth author was supported by the ERC CZ grant LL1203 of the Czech Ministry of Education.

Received 11 April 2017

Published 1 February 2019