Thin sets in trigonometrical series and quasinormal convergence
Tiling and spectral properties of near-cubic domains
We prove that if a measurable domain tiles ℝ or ℝ² by translations, and if it is "close enough" to a line segment or a square respectively, then it admits a lattice tiling. We also prove a similar result for spectral sets in dimension 1, and give an example showing that there is no analogue of the tiling result in dimensions 3 and higher.
Time-frequency analysis of Sjöstrand's class.
We investigate the properties an exotic symbol class of pseudodifferential operators, Sjöstrand's class, with methods of time-frequency analysis (phase space analysis). Compared to the classical treatment, the time-frequency approach leads to striklingly simple proofs of Sjöstrand's fundamental results and to far-reaching generalizations.
Topics on analytic sets
Topological Dichotomy and Unconditional Convergence
In this paper, we give a criterion for unconditional convergence with respect to some summability methods, dealing with the topological size of the set of choices of sign providing convergence. We obtain similar results for boundedness. In particular, quasi-sure unconditional convergence implies unconditional convergence.
Topological results on sequences and their applications in the theory of trigonometric series
Trace Inequalities, Maximal Inequalities, and Weighted Fourier Transform Estimates.
Traces and the F. and M. Riesz theorem for vector fields
This work studies conditions that insure the existence of weak boundary values for solutions of a complex, planar, smooth vector field . Applications to the F. and M. Riesz property for vector fields are discussed.
Transformadas de Fourier de distribuciones homogeneas
Transformation de Fourier sur les espaces
Nous étudions d’abord la transformation de Fourier sur les espaces qui sont formés de fonctions appartenant localement à et se comportant à l’infini comme des éléments de . Si , les transformées de Fourier des éléments de appartiennent à . Dans les autres cas, nous donnons quelques résultats partiels.Nous montrons ensuite que est le plus grand espace vectoriel solide de fonctions mesurables sur lequel la transformation de Fourier puisse se définir par prolongement par continuité.
Transforms of Vector-Valued Functions and Measures
Translation and power independence for Bernoulli convolutions
Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1
We study convolution operators bounded on the non-normable Lorentz spaces of the real line and the torus. Here 0 < q < 1. On the real line, such an operator is given by convolution with a discrete measure, but on the torus a convolutor can also be an integrable function. We then give some necessary and some sufficient conditions for a measure or a function to be a convolutor on . In particular, when the positions of the atoms of a discrete measure are linearly independent over the rationals,...
Transplantation operators and Cesàro operators for the Hankel transform
The transplantation operators for the Hankel transform are considered. We prove that the transplantation operator maps an integrable function under certain conditions to an integrable function. As an application, we obtain the L¹-boundedness and H¹-boundedness of Cesàro operators for the Hankel transform.
Transplanting Maximal Inequalities Between Laguerre and Hankel Multipliers.
Trigonometric approximation by Nörlund type means in -norm
We show that the same degree of approximation as in the theorems proved by L. Leindler [Trigonometric approximation in -norm, J. Math. Anal. Appl. 302 (2005), 129–136] and P. Chandra [Trigonometric approximation of functions in -norm, J. Math. Anal. Appl. 275 (2002), 13–26] is valid for a more general class of lower triangular matrices. We also prove that these theorems are true under weakened assumptions.
Trigonometric approximation in the norms and seminorm
Trigonometric interpolation for bivariate functions of bounded variation
Trigonometric interpolation, III
Trigonometric interpolation, IV