9 papers
Limiting absorption principle for time-harmonic elastic scattering of plane waves from diffraction gratings
Jianli Xiang, Guanghui Hu
We establish the limiting absorption principle for time-harmonic elastic scattering of plane waves by a periodic rigid diffraction grating. By perturbing the frequency with a small…
A Critical-Scale Extension of Zhizhiashvili's Theorem for Rectangular Fourier Series
Ushangi Goginava
We address a long-standing endpoint problem arising from Zhizhiashvili's logarithmic modulus theorem for multiple Fourier series. We prove an endpoint Dini criterion for almost-eve…
An Oskolkov--Zhizhiashvili Criterion for Rectangular Fourier Sums
Ushangi Goginava
Let denote the symmetric rectangular partial sums of the trigonometric Fourier series of a function on the -dimensional torus. We prove a summable endpoint crit…
Almost everywhere divergence of double Fourier series along shrinking conical regions
Ushangi Goginava
We study almost everywhere divergence of rectangular partial sums of double trigonometric Fourier series along variable regions concentrated near the diagonal. Fefferman's theorem…
Dyadic Martingale Transforms and Weighted Walsh-Carleson Operators
Ushangi Goginava, Farrukh Mukhamedov
We study weighted Walsh--Carleson maximal operators arising from dyadic martingale transforms associated with Walsh--Fourier partial sums. For weights satisfying a uniform dyadic v…
Almost Everywhere Convergence of Arithmetic Means of Walsh--Fourier Partial Sums Along Subsequences
Ushangi Goginava
Let denote the -th partial sum of the Walsh-Fourier series of . For an increasing sequence of positive integers, consider the arithmetic…