10 citations · 31 across the 14 of their papers we have counts for
17 papers
Discrete Gaussian Free Field via Hadamard's formula
Haakan Hedenmalm, Pavel Mozolyako, Daniil Panov
We present a novel way of constructing the Gaussian Free Field on a weighted graph via a dynamical expansion of the Green function along an expanding family of subgraphs. Along the…
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…
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…
Multi-parameter Carleson embeddings for on or for on , 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 case to either or . This is in striking diffe…
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…
Carleson embedding on tri-tree and on tri-disc
Pavel Mozolyako, Georgios Psaromiligkos, Alexander Volberg +1
We prove multi-parameter dyadic embedding theorem for Hardy operator on the multi-tree. We also show that for a large class of Dirichlet spaces in bi-disc and tri-disc this proves…
Counterexamples for bi-parameter Carleson embedding
Pavel Mozolyako, Georgios Psaromiligkos, Alexander Volberg
We build here several counterexamples for two weight bi-parameter Carleson embedding theorem.
Bi-parameter Carleson embeddings with product weights
Nicola Arcozzi, Pavel Mozolyako, Georgios Psaromiligkos +2
Coifman--Meyer multipliers represent a very important class of bi-linear singular operators, which were extensively studied and generalized. They have a natural multi-parameter cou…
Oscillation of Functions in the Hölder class
Pavel Mozolyako, Artur Nicolau
We study the size of the set of points where the -divided difference of a function in the Hölder class is bounded below by a fixed positive constant. Our results are obtai…
Some properties related to trace inequalities for the multi-parameter Hardy operators on poly-trees
Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt
In this note we investigate the multi-parameter Potential Theory on the weighted -tree (Cartesian product of several copies of uniform dyadic tree), which is connected to the di…
Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc
Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt +1
We characterize the Carleson measures for the Dirichlet space on the bidisc, hence also its multiplier space. Following Maz'ya and Stegenga, the characterization is given in terms…
Bi-parameter embedding and measures with restriction energy condition
Nicola Arcozzi, Irina Holmes, Pavel Mozolyako +1
Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt, and Giulia Sarfatti recently gave the proof of a bi-parameter Carleson embedding theorem. Their proof uses heavily the notion…
Bellman function sitting on a tree
Nicola Arcozzi, Irina Holmes, Pavel Mozolyako +1
In this note we give a proof-by-formula of certain important embedding inequalities on dyadic tree. This is done with the help of Bellman function. We also consider the case of a b…
Some Hilbert Spaces related with the Dirichlet space
Nicola Arcozzi, Karl-Mikael Perfekt, Pavel Mozolyako +2
We do a preliminary study of the reproducing kernel Hilbert space having as kernel , where is a positive integer and is the reproducing kernel of the analytic Dirichle…
Boundary oscillations of harmonic functions in Lipschitz domains
Pavel Mozolyako
Let be a harmonic function in the halfspace that grows near the boundary not faster than some fixed majorant . Recently it was prove…
On a theorem of M. Cartwright in higher dimensions
A. Logunov, E. Malinnikova, P. Mozolyako
We consider harmonic functions in the unit ball of that are unbounded near the boundary but can be estimated from above by some (rapidly increasing) radial weigh…
Wavelet decomposition of harmonic functions in growth spaces
Kjersti Solberg Eikrem, Eugenia Malinnikova, Pavel A. Mozolyako
Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove…