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Mathematical Analysis. - Two-weight dyadicHardy inequalities.

Authors :
ARCOZZI, NICOLA
CHALMOUKIS, NIKOLAOS
LEVI, MATTEO
MOZOLYAKO, PAVEL
Source :
Rendiconti Lincei - Matematica e Applicazioni; 2023, Vol. 34 Issue 3, p657-714, 58p
Publication Year :
2023

Abstract

We present various results concerning the two-weight Hardy inequality on infinite trees. Our main aim is to survey known characterizations (and proofs) for trace measures, as well as to provide some new ones. Also for some of the known characterizations we provide here new proofs. In particular, we obtain a new characterization in terms of a reverse Hölder inequality for trace measures, and one based on the well-known Muckenhoupt-Wheeden-Wolff inequality, of which we here give a new probabilistic proof. We provide a new direct proof for the so-called isocapacitary characterization and a new simple proof, based on a monotonicity argument, for the so-called mass-energy characterization. Furthermore, we introduce a conformally invariant version of the two-weight Hardy inequality, characterize the compactness of the Hardy operator, provide a list of open problems, and suggest some possible lines of future research. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
11206330
Volume :
34
Issue :
3
Database :
Complementary Index
Journal :
Rendiconti Lincei - Matematica e Applicazioni
Publication Type :
Academic Journal
Accession number :
174481344
Full Text :
https://doi.org/10.4171/RLM/1023