Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 10, Number 1 (2019), 29-45.
The rate of almost-everywhere convergence of Bochner–Riesz means on Sobolev spaces
We investigate the convergence rate of the generalized Bochner–Riesz means on -Sobolev spaces in the sharp range of and (). We give the relation between the smoothness imposed on functions and the rate of almost-everywhere convergence of . As an application, the corresponding results can be extended to the -torus by using some transference theorems. Also, we consider the following two generalized Bochner–Riesz multipliers, and , where , , are positive real numbers. We prove that, as the maximal operators of the multiplier operators with respect to the two functions, their -boundedness is equivalent for any , and fixed .
Ann. Funct. Anal., Volume 10, Number 1 (2019), 29-45.
Received: 3 November 2017
Accepted: 11 February 2018
First available in Project Euclid: 16 January 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 42B15: Multipliers
Secondary: 41A35: Approximation by operators (in particular, by integral operators) 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 47B38: Operators on function spaces (general)
Zhao, Junyan; Fan, Dashan. The rate of almost-everywhere convergence of Bochner–Riesz means on Sobolev spaces. Ann. Funct. Anal. 10 (2019), no. 1, 29--45. doi:10.1215/20088752-2018-0006. https://projecteuclid.org/euclid.afa/1547629221