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arXiv · 1112.1744

Weighted bounds for variational Walsh-Fourier series

Michael T. Lacey·Yen Do
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Abstract

For 1<p<infty, and weight w in A_p, and function f in L^p(w), we show that the r-variation of the Walsh-Fourier sums are finite, for r sufficiently large as function of w. (That r is a function of w is necessary.) This strengthens a result of Hunt-Young and is a weighted extension of a variation norm Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses phase plane analysis and a weighted extension of a variational inequality of Lepingle.

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BibTeXRIS

Michael T. Lacey, Yen Do. 2012-02-12. Weighted bounds for variational Walsh-Fourier series. https://arxiv.org/abs/1112.1744

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