Geodesic
Weighted Hardy inequalities and Hardy transforms of weights
Studia Mathematica, Tome 139 (2000) no. 2, pp. 189-196

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $A_{p+1}$
DOI : 10.4064/sm-139-2-189-196
Keywords: Hardy's inequalities, Hardy transform, weights

Joan Cerdà 1 ;  1

1 
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Joan Cerdà;  . Weighted Hardy inequalities and Hardy transforms of weights. Studia Mathematica, Tome 139 (2000) no. 2, pp. 189-196. doi: 10.4064/sm-139-2-189-196

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