# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Weighted Hardy inequalities and Hardy transforms of weights

### Tom 139 / 2000

Studia Mathematica 139 (2000), 189-196 DOI: 10.4064/sm-139-2-189-196

#### Streszczenie

Many problems in analysis are described as weighted norm inequalities that have given rise to different classes of weights, such as $A_p$-weights of Muckenhoupt and $B_p$-weights of Ariño and Muckenhoupt. Our purpose is to show that different classes of weights are related by means of composition with classical transforms. A typical example is the family $M_p$ of weights w for which the Hardy transform is $L_p(w)$-bounded. A $B_p$-weight is precisely one for which its Hardy transform is in $M_p$, and also a weight whose indefinite integral is in $A_{p+1}$

• Joan Cerdà

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