Weighted norm inequalities for maximal operator of Fourier series

Article Type

Research Article

Publication Title

Advances in Operator Theory


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.



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