Sharp L p -weighted Sobolev inequalities

Carlos Pérez

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 3, page 809-824
  • ISSN: 0373-0956

Abstract

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We prove sharp weighted inequalities of the form ∫ R n | f ( x ) | p v ( x ) d x ≤ C ∫ R n | q ( D ) ( f ) ( x ) | p N ( v ) ( x ) d x where q ( D ) is a differential operator and N is a combination of maximal type operator related to q ( D ) and to p .

How to cite

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Pérez, Carlos. "Sharp $L^p$-weighted Sobolev inequalities." Annales de l'institut Fourier 45.3 (1995): 809-824. <http://eudml.org/doc/75139>.

@article{Pérez1995,
abstract = {We prove sharp weighted inequalities of the form\begin\{\}\int \_\{\{\bf R\}^n\}\vert f(x)\vert ^p v(x)dx\le C\int \_\{\{\bf R\}^n\}\vert q(D)(f)(x)\vert ^p N(v)(x)dx\end\{\}where $q(D)$ is a differential operator and $N$ is a combination of maximal type operator related to $q(D)$ and to $p$.},
author = {Pérez, Carlos},
journal = {Annales de l'institut Fourier},
keywords = {weighted inequalities; Sobolev inequalities; fractional integrals; maximal type operator},
language = {eng},
number = {3},
pages = {809-824},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sharp $L^p$-weighted Sobolev inequalities},
url = {http://eudml.org/doc/75139},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Pérez, Carlos
TI - Sharp $L^p$-weighted Sobolev inequalities
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 3
SP - 809
EP - 824
AB - We prove sharp weighted inequalities of the form\begin{}\int _{{\bf R}^n}\vert f(x)\vert ^p v(x)dx\le C\int _{{\bf R}^n}\vert q(D)(f)(x)\vert ^p N(v)(x)dx\end{}where $q(D)$ is a differential operator and $N$ is a combination of maximal type operator related to $q(D)$ and to $p$.
LA - eng
KW - weighted inequalities; Sobolev inequalities; fractional integrals; maximal type operator
UR - http://eudml.org/doc/75139
ER -

References

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