Tbilisi Analysis and PDE Seminar Extended Abstracts of the 2020-2023 Seminar Talks

The aim of this volume is to present some new developments and ideas in partial differential equations and mathematical analysis, including spectral analysis and boundary value problems for PDE, harmonic analysis, inequalities, integral equations, and applications. This book is a collection of short summaries of reports from lectures delivered at Tbilisi Analysis & PDE seminars and workshops. In particular, it contains some applications and several open questions aimed at inspiring further research. The volume contains 21 research articles.

- Continuous inequalities: introduction, examples and related topics.- Approximation by Vilenkin-Nörlund Means in Lebesgue Spaces.- On Divergence of Fejér Means with Respect to Walsh System on sets of Measure Zero.- Martingale Hardy Spaces and Some Maximal Operators Associated with Walsh- Fejér Means.- Generic Bessel potential spaces on Lie groups.- The finite Hilbert transform acting in rearrangement invariant spaces on (-1, 1).- The Banach Gelfand triple and its role in classical Fourier analysis and operator theory.- A note on a frictional unilateral contact problem in nonlinear elasticity.- Maximal noncompactness of singular integral operators on Lp spaces with power weights.- A remark on piecewise linear interpolation of continuous Fourier multipliers.- Banach algebras of convolution type operators with PQC data.- Integrability and convergence of trigonometric series and Fourier transforms.- Commutators of Calderón–Zygmund Operators in Grand Variable Exponent Morrey Spaces, and Applications to PDEs.- Symmetric Stein–Tomas, and why do we care?.- On Solonnikov parabolicity of the evolution anisotropic Stokes and Oseen PDE systems.- On Convergence and Divergence of Fourier Series and Fejér Means with Applications to Lebesgue and Vilenkin-Lebesgue Points.- On generalized sharpness of some Hardy-type inequalities.- Interaction problems for n-dimensional Dirac operators with singular potentials.- Convergence and summability in classical and martingale Hardy spaces.- Modulus of Continuity and Convergence of Fejér Means of Vilenkin-Fourier Series in the Variable Martingale Hardy Space Hp(·).- On unconditional convergence of Fourier series with respect to general orthonormal systems.

Roland Duduchava is a professor of mathematics, the director of the Institute of Mathematics and the head of the PhD program “Applied Mathematics”  at the University of Georgia.

Eugene Shargorodsky is a professor of mathematics at King’s College London.

George Tephnadze is a scientific fellow at the Institute of Mathematics and the head of the master’s program “Pure and Applied Mathematics” at the University of Georgia, Georgia.