13 citations · 13 across the 30 of their papers we have counts for
35 papers
A Counterexample to Belinsky's Conjecture on Cesàro Means at Lebesgue Points
Ushangi Goginava
In 1997, Belinsky conjectured that, for convex subsequences, the logarithmic growth condition of Carleson, Trigub, and Zagorodni\uı is necessary and sufficient for the arithmetic m…
Cesaro Means along Polynomial Subsequences of Fourier Partial Sums at Lebesgue Points
Ushangi Goginava
In 1936, Zalcwasser proved the almost everywhere convergence of the arithmetic means of the square subsequence of trigonometric Fourier partial sums and asked whether this result e…
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…