$(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative

Ferenc Weisz

ArticleOriginal scientific text

Title

$(H_{p}, L_{p})$ -type inequalities for the two-dimensional dyadic derivative

Authors ¹

Affiliations

Department of Numerical Analysis, Eötvös L. University, Múzeum krt. 6-8, H-1088 Budapest, Hungary

Abstract

It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space

H_{p, q}

to

L_{p, q}

(2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type

(L_{1}, L_{1})

. As a consequence we show that the dyadic integral of a ∞ function

f \in L_{1}

is dyadically differentiable and its derivative is f a.e.

Keywords

ENG

Hardy spaces, p-atom, interpolation, Walsh functions, dyadic derivative

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Title

(Hp,Lp)-type inequalities for the two-dimensional dyadic derivative

Affiliations

Abstract

Keywords

Bibliography

$(H_{p}, L_{p})$ -type inequalities for the two-dimensional dyadic derivative