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Volume 38, Issue 4
First Order Hardy Inequalities Revisited

Xia Huang & Dong Ye

DOI: 10.4208/cmr.2021-0085

Commun. Math. Res., 38 (2022), pp. 535-559.

Published online: 2022-10

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  • Abstract

In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants, but also supplies improved or new estimates in miscellaneous situations, such as multipolar potential, the exponential weight, hyperbolic space, Heisenberg group, the edge Laplacian, or the Grushin type operator.

  • Keywords

First order Hardy inequality, inequality via equality, generalized Bessel pair.

  • AMS Subject Headings

26D10, 35A23, 31C12, 46E35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-38-535, author = {Huang , Xia and Ye , Dong}, title = {First Order Hardy Inequalities Revisited}, journal = {Communications in Mathematical Research }, year = {2022}, volume = {38}, number = {4}, pages = {535--559}, abstract = {

In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants, but also supplies improved or new estimates in miscellaneous situations, such as multipolar potential, the exponential weight, hyperbolic space, Heisenberg group, the edge Laplacian, or the Grushin type operator.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0085}, url = {http://global-sci.org/intro/article_detail/cmr/21071.html} }
TY - JOUR T1 - First Order Hardy Inequalities Revisited AU - Huang , Xia AU - Ye , Dong JO - Communications in Mathematical Research VL - 4 SP - 535 EP - 559 PY - 2022 DA - 2022/10 SN - 38 DO - http://doi.org/10.4208/cmr.2021-0085 UR - https://global-sci.org/intro/article_detail/cmr/21071.html KW - First order Hardy inequality, inequality via equality, generalized Bessel pair. AB -

In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants, but also supplies improved or new estimates in miscellaneous situations, such as multipolar potential, the exponential weight, hyperbolic space, Heisenberg group, the edge Laplacian, or the Grushin type operator.

Huang , Xia and Ye , Dong. (2022). First Order Hardy Inequalities Revisited. Communications in Mathematical Research . 38 (4). 535-559. doi:10.4208/cmr.2021-0085
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