Displaying similar documents to “Two-parameter Hardy-Littlewood inequality and its variants”

On the characterization of Hardy-Besov spaces on the dyadic group and its applications

Jun Tateoka (1994)

Studia Mathematica

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C. Watari [12] obtained a simple characterization of Lipschitz classes L i p ( p ) α ( W ) ( 1 p , α > 0 ) on the dyadic group using the L p -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces B p , q α on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces B p , q α by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality...

On (C,1) summability of integrable functions with respect to the Walsh-Kaczmarz system

G. Gát (1998)

Studia Mathematica

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Let G be the Walsh group. For f L 1 ( G ) we prove the a. e. convergence σf → f(n → ∞), where σ n is the nth (C,1) mean of f with respect to the Walsh-Kaczmarz system. Define the maximal operator σ * f s u p n | σ n f | . We prove that σ* is of type (p,p) for all 1 < p ≤ ∞ and of weak type (1,1). Moreover, σ * f 1 c | f | H , where H is the Hardy space on the Walsh group.

Nonconvolution transforms with oscillating kernels that map 1 0 , 1 into itself

G. Sampson (1993)

Studia Mathematica

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We consider operators of the form ( Ω f ) ( y ) = ʃ - Ω ( y , u ) f ( u ) d u with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and h L (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space 1 0 , 1 (= B) into itself. In particular, all operators with h ( y ) = e i | y | a , a > 0, a ≠ 1, map B into itself.

The value-distribution of lacunary series and a conjecture of Paley

Takafumi Murai (1981)

Annales de l'institut Fourier

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The purpose of this paper is to establish a theorem which answers a conjecture of Paley on the distribution of values of Hadamard lacunary series and which is useful to study the Peano curve property of such series.