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Dyn’kin, E. M.; Osilenker, B. P.

Weighted estimates of singular integrals and their applications. (English. Russian original) Zbl 0568.42009

J. Sov. Math. 30, 2094-2154 (1985); translation from Itogi Nauki Tekh., Ser. Mat. Anal. 21, 42-129 (1983).
This paper is a survey of some recent developments in the theory of weighted estimates of the form \[ \int_{{\mathbb{R}}^ n}| Tf|^ pw\leq C\int_{{\mathbb{R}}^ n}| f|^ pv \] and corresponding inequalities of the weak type \[ \int_{\{| T(f)| >\lambda \}}w\leq C1/| \lambda |^ p\int_{{\mathbb{R}}^ n}| f|^ pv,\quad \lambda >0, \] where T is a singular integral or maximal operator and v, w are weighted functions for which known conditions \((A_ p)\) are fulfilled.
The following problems determine the content of the paper: Hardy inequalities, Stieltjes transform, weighted estimates of maximal function, fractional integrals, singular operators and integrals of Cauchy type.
Reviewer: A.G.Baskakov

Cited in 1 Review
Cited in 15 Documents

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
47A30 Norms (inequalities, more than one norm, etc.) of linear operators

Keywords:

bibliography; weighted estimates; singular integral; maximal operator; Hardy inequalities
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Full Text: DOI

References:

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