# Weighted Hardy inequalities and Hardy transforms of weights

Studia Mathematica (2000)

- Volume: 139, Issue: 2, page 189-196
- ISSN: 0039-3223

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topCerdà, Joan, and Martín, Joaquim. "Weighted Hardy inequalities and Hardy transforms of weights." Studia Mathematica 139.2 (2000): 189-196. <http://eudml.org/doc/216718>.

@article{Cerdà2000,

abstract = {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 $A_\{p+1\}$},

author = {Cerdà, Joan, Martín, Joaquim},

journal = {Studia Mathematica},

keywords = {Hardy's inequalities; Hardy transform; weights; Hardy inequalities; Hardy-Littlewood maximal operator; weighted Lebesgue spaces; Hardy operator; Muckenhoupt class},

language = {eng},

number = {2},

pages = {189-196},

title = {Weighted Hardy inequalities and Hardy transforms of weights},

url = {http://eudml.org/doc/216718},

volume = {139},

year = {2000},

}

TY - JOUR

AU - Cerdà, Joan

AU - Martín, Joaquim

TI - Weighted Hardy inequalities and Hardy transforms of weights

JO - Studia Mathematica

PY - 2000

VL - 139

IS - 2

SP - 189

EP - 196

AB - 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 $A_{p+1}$

LA - eng

KW - Hardy's inequalities; Hardy transform; weights; Hardy inequalities; Hardy-Littlewood maximal operator; weighted Lebesgue spaces; Hardy operator; Muckenhoupt class

UR - http://eudml.org/doc/216718

ER -

## References

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- [Mu1] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. Zbl0236.26016
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- [Ne1] C. J. Neugebauer, Weighted norm inequalities for averaging operators of monotone functions, Publ. Mat. 35 (1991), 429-447. Zbl0746.42014
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