Singular integrals on product domains

Abstract

It is proved that under some conditions the singular integral T is bounded from the Hardy spaceThe multiplier transforms, especially the Riesz transforms and their boundedness on H p (R d 1 × . . . × R d k ) are also investigated.

Summability of Multi-Dimensional Trigonometric Fourier Series

“…, d, let f (j 1 ,...,j d ) = f . The following result can be found in Gundy and Stein [47,46], Chang and Fefferman [22] and Weisz [93,94].…”

Pointwise summability of Vilenkin--Fourier series

“…where G 2 is a Walsh group. Weisz proved in [12] that a.e. point x ∈ G 2 is a Walsh-Lebesgue point of an integrable function f .…”

“…Denote by f = (f (n,k) , n, k ∈ N) a martingale with respect to (F n,k , n, k ∈ N) (for details see, e.g. [12], [15]).…”

Matrix transformations of sequences and applications in Fourier analysis

“…Weisz introduced the one-dimensional Walsh-Lebesgue point in [34] : is a Walsh-Lebesgue point of , if where is a Walsh group. Weisz proved in [34] that a.e. point is a Walsh-Lebesgue point of an integrable function f .…”