P. Mozolyako

activity

20122026

most citedBi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc

10 citations · 31 across the 14 of their papers we have counts for

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Showing 2021Show all

4 papers · 1 filter

math.CA2021★ 3 cited

Two-weight dyadic Hardy's inequalities

Nicola Arcozzi, Nikolaos Chalmoukis, Matteo Levi +1

We present various results concerning the two-weight Hardy's inequality on infinite trees. Our main scope is to survey known characterizations (and proofs) for trace measures, as w…

math.AP2021

Differences between the potential theories on a tree and on a bi-tree

Pavel Mozolyako, Alexander Volberg

In this note we give several counterexamples. One shows that small energy majorization on bi-tree fails. The second counterexample shows that partial energy estimate always valid o…

math.CA2021

Multi-parameter Carleson embeddings for $p \neq = 2$ on $T^{2}$ or for $p = 2$ on $T^{4}$ , and why the proofs fail

P. Mozolyako, G. Psaromiligkos, A. Volberg

This note contains a plethora of counterexamples to attempts to generalize the results of bi-parameter embedding from $p = 2$ case to either $p > 2$ or $p < 2$ . This is in striking diffe…

math.AP2021★ 3 cited

Improved surrogate bi-parameter maximum principle

Pavel Mozolyako, Georgios Psaromiligkos, Alexander Volberg +1

Logarithmic potentials and many other potentials satisfy maximum principle. The dyadic version of logarithmic potential can be easily introduced, it lives on dyadic tree and also s…

Two-weight dyadic Hardy's inequalities

Differences between the potential theories on a tree and on a bi-tree

Multi-parameter Carleson embeddings for p=2 on T2 or for p=2 on T4, and why the proofs fail

Improved surrogate bi-parameter maximum principle

Multi-parameter Carleson embeddings for $p \neq = 2$ on $T^{2}$ or for $p = 2$ on $T^{4}$ , and why the proofs fail