$L^p$ weighted inequalities for the dyadic square function

Akihito Uchiyama

ArticleOriginal scientific text

Title

$L^{p}$ weighted inequalities for the dyadic square function

Authors ¹

Affiliations

Mathematics Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai-shi, 980, Japan

Abstract

We prove that

ʃ {(S_{d} f)}^{p} V d x \leq C_{p, n} ʃ {| f |}^{p} M_{d}^{([\frac{p}{2}] + 2)} V d x

, where

S_{d}

is the dyadic square function,

M_{d}^{(k)}

is the k-fold application of the dyadic Hardy-Littlewood maximal function and p > 2.

Keywords

ENG

dyadic square function, dyadic maximal function, weighted inequality

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Title

Lp weighted inequalities for the dyadic square function

Affiliations

Abstract

Keywords

Bibliography

$L^{p}$ weighted inequalities for the dyadic square function