7 papers
On the Bourgain--Brezis--Mironescu spaces over Carleson tents
Árpád Bényi, Bingyang Hu, Xiaojing Zhou
We introduce Carleson analogs of the Bourgain--Brezis--Mironescu spaces and by measuring mean oscillation over upper Carleson tents. For these spaces, denoted by $B_{\mat…
The Bilinear Hilbert-Carleson operator along curves. The purely non-zero curvature case
Árpád Bényi, Bingyang Hu, Victor Lie
In this paper, we provide the maximal boundedness range (up to end-points) for the Bilinear Hilbert-Carleson operator along curves in the (purely) non-zero curvature setting. More…
Modulation spaces with scaling symmetry
Árpád Bényi, Tadahiro Oh
We indicate how to construct a family of modulation function spaces that have a scaling symmetry. We also illustrate the behavior of the Schrödinger multiplier on such function spa…
On the probabilistic Cauchy theory for nonlinear dispersive PDEs
Árpád Bényi, Tadahiro Oh, Oana Pocovnicu
In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.
Strongly singular bilinear Calderón-Zygmund operators and a class of bilinear pseudodifferential operators
Árpád Bényi, Lucas Chaffee, Virginia Naibo
Motivated by the study of kernels of bilinear pseudodifferential operators with symbols in a Hörmander class of critical order, we investigate boundedness properties of strongly si…
Linear and bilinear theorems à la Stein
Árpád Bényi, Tadahiro Oh
In this work, we state and prove versions of the linear and bilinear theorems involving quantitative estimates, analogous to the quantitative linear theorem due to St…
Modulation spaces, Wiener amalgam spaces, and Brownian motions
Árpád Bényi, Tadahiro Oh
We study the local-in-time regularity of the Brownian motion with respect to localized variants of modulation spaces M^{p, q}_s and Wiener amalgam spaces W^{p, q}_s. We show that t…