Weighted norm inequalities for maximal operator of Fourier series
Article Type
Research Article
Publication Title
Advances in Operator Theory
Abstract
Let M be the maximal partial sum operator for Fourier series on the ring of integers D of a local field K. For 1 < p< ∞, we establish weighted norm inequalities for M on the weighted spaces Lp(D, w) , where w is a Muckenhoupt Ap weight. As a consequence of this result, we prove that the Fourier partial sum operators are uniformly of weak type (1, 1) on L1(D). Further, we establish vector-valued inequalities for Fourier series on D. These results include the cases when D is the ring of integers of the p-adic field Qp and the field Fq((X)) of formal Laurent series over a finite field Fq, and in particular, when D is the Walsh-Paley or dyadic group 2 ω.
DOI
10.1007/s43036-021-00181-y
Publication Date
1-1-2022
Recommended Citation
Molla, Md Nurul and Behera, Biswaranjan, "Weighted norm inequalities for maximal operator of Fourier series" (2022). Journal Articles. 3392.
https://digitalcommons.isical.ac.in/journal-articles/3392
