Árpád Bényi

Local well-posedness of nonlinear dispersive equations on modulation spaces

By using tools of time-frequency analysis, we obtain some improved local well-posedness results for the NLS, NLW and NLKG equations with Cauchy data in modulation spaces

Best constants for certain multilinear integral operators

M{p, 1}_{0,s}

Sobolev space estimates and symbolic calculus for bilinear pseudodifferential operators

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Compact Bilinear Operators and Commutators

We provide explicit formulas in terms of the special function gamma for the best constants in nontensorial multilinear extensions of some classical integral inequalities due to Hilbert, Hardy, and Hardy-Littlewood-Pólya.

The Sobolev Inequality on the Torus Revisited

Bilinear operators are investigated in the context of Sobolev spaces and various techniques useful in the study of their boundedness properties are developed. In particular, several classes of symbols for bilinear operators beyond the so-called Coifman-Meyer class are considered. Some of the Sobolev space estimates obtained apply to both the bilinear Hilbert transform and its singular multipliers generalizations as well as to operators with variable dependent symbols. A symbolic calculus for the transposes of bilinear pseudodifferential operators and for the composition of linear and bilinear pseudodifferential operators is presented too.

Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS

First published in Proceedings of the American Mathematical Society, volume 141, published by the American Mathematical Society. Also available electronically from http://www.ams.org/journals/proc/2013-141-10/S0002-9939-2013-11689-8/home.html

A generalization of Routh's triangle theorem

We revisit the Sobolev inequality for periodic functions on the d-dimensional torus. We provide an elementary Fourier analytic proof of this inequality which highlights both the similarities and differences between the periodic setting and the classical ddimensional Euclidean one.

On a Class of Bilinear Pseudodifferential Operators

We introduce a randomization of a function on \( \mathbb{R}^{d} \) that is naturally associated to the Wiener decomposition and, intrinsically, to the modulation spaces. Such randomized functions enjoy better integrability, thus allowing us to improve the Strichartz estimates for the Schrodinger equation. As an example, we also show that the energy-critical cubic nonlinear Schrodinger equation on \( \mathbb{R}^{4} \) is almost surely locally well posed with respect to randomized initial data below the energy space.

Outer Median Triangles

Abstract We prove a generalization of the well-known Rouths triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynmans triangle is also given.

Unimodular Fourier multipliers for modulation spaces

We provide a direct proof for the boundedness of pseudodifferential operators with symbols in the bilinear Hörmander class , . The proof uses a reduction to bilinear elementary symbols and Littlewood-Paley theory.