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math.CA2011★ 1 cited
Weighted bounds for variational Walsh-Fourier series
Michael T. Lacey, Yen Do
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…
math.CA2011★ 19 cited
On the Convergence of Lacunary Walsh-Fourier Series
Yen Do, Michael T. Lacey
We study the Walsh-Fourier series of S_{n_j}f, along a lacunary subsequence of integers {n_j}. Under a suitable integrability condition, we show that the sequence converges to f a.…