Hardy and Rellich type inequalities with remainders

Ramil Nasibullin

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 1, page 87-110
  • ISSN: 0011-4642

Abstract

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Hardy and Rellich type inequalities with an additional term are proved for compactly supported smooth functions on open subsets of the Euclidean space. We obtain one-dimensional Hardy type inequalities and their multidimensional analogues in convex domains with the finite inradius. We use Bessel functions and the Lamb constant. The statements proved are a generalization for the case of arbitrary $p\geq 2$ of the corresponding inequality proved by F. G. Avkhadiev, K.-J. Wirths (2011) for $p = 2$. Also we establish Rellich type inequalities on arbitrary domains, regular sets, on domains with $\theta $-cone condition and on convex domains.

How to cite

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Nasibullin, Ramil. "Hardy and Rellich type inequalities with remainders." Czechoslovak Mathematical Journal 72.1 (2022): 87-110. <http://eudml.org/doc/297621>.

@article{Nasibullin2022,
abstract = {Hardy and Rellich type inequalities with an additional term are proved for compactly supported smooth functions on open subsets of the Euclidean space. We obtain one-dimensional Hardy type inequalities and their multidimensional analogues in convex domains with the finite inradius. We use Bessel functions and the Lamb constant. The statements proved are a generalization for the case of arbitrary $p\geq 2$ of the corresponding inequality proved by F. G. Avkhadiev, K.-J. Wirths (2011) for $p = 2$. Also we establish Rellich type inequalities on arbitrary domains, regular sets, on domains with $\theta $-cone condition and on convex domains.},
author = {Nasibullin, Ramil},
journal = {Czechoslovak Mathematical Journal},
language = {eng},
number = {1},
pages = {87-110},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Hardy and Rellich type inequalities with remainders},
url = {http://eudml.org/doc/297621},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Nasibullin, Ramil
TI - Hardy and Rellich type inequalities with remainders
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 1
SP - 87
EP - 110
AB - Hardy and Rellich type inequalities with an additional term are proved for compactly supported smooth functions on open subsets of the Euclidean space. We obtain one-dimensional Hardy type inequalities and their multidimensional analogues in convex domains with the finite inradius. We use Bessel functions and the Lamb constant. The statements proved are a generalization for the case of arbitrary $p\geq 2$ of the corresponding inequality proved by F. G. Avkhadiev, K.-J. Wirths (2011) for $p = 2$. Also we establish Rellich type inequalities on arbitrary domains, regular sets, on domains with $\theta $-cone condition and on convex domains.
LA - eng
UR - http://eudml.org/doc/297621
ER -

References

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