×

Maximal \((C,\alpha,\beta)\) operators of two-dimensional Walsh-Fourier series. (English) Zbl 1164.42320

Summary: The main aim of this paper is to prove that for the boundedness of the maximal operator \(\sigma^{\alpha,\beta}_*\) from the Hardy space \(H_p(I^2)\) to the space \(L_p(I_2)\) the assumption \(p>\max\{1/(\alpha+1),1/(\beta+1)\}\) is essential.

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
PDFBibTeX XMLCite
Full Text: EuDML