Spherical harmonics and maximal estimates for the Schrödinger equation.
L... maximal estimates for solutions to the Schrödinger equation.
Norm Inequalities for Spherical Means.
Regularity and Integrability of Spherical Means.
An Hp Inequality for Strongly Singular Integrals.
Two theorems on convergence of Fourier integrals and Fourier series
Global maximal estimates for solutions to the Schrödinger equation
Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.
Spherical harmonics and spherical averages of Fourier transforms
Fourier multipliers and estimates of the Fourier transform of measures carried by smooth curves in R²
A relation between Fourier transforms in one and two variables
Convergence of generalized conjugate partial sums of Fourier series.
Generalized conjugate partial sums of Fourier series are used to find jumps of functions. The rate of convergence is studied and sharp results are obtained.
A Littlewood-Paley Inequality for the Carleson Operator.
Oscillatory integrals and multiplier problem for the disc
Remarks on a theorem by N. Yu. Antonov
We extend some results of N. Yu. Antonov on convergence of Fourier series to more general settings. One special feature of our work is that we do not assume smoothness for the kernels in our hypotheses. This has interesting applications to convergence with respect to general orthonormal systems, like the Walsh-Fourier system, for which we prove a.e. convergence in the class L log L log log log L. Other applications are given in the theory of differentiation of integrals.
Some remarks on restriction of the Fourier tranform for general measures.
In this paper we establish a formal connection between the average decay of the Fourier transform of functions with respect to a given measure and the of that measure. We also present a generalization of the classical restriction theorem of Stein and Tomas replacing the sphere with sets of prefixed Hausdorff dimension n - 1 + α, with 0 < α < 1.
Littlewood-Paley decompositions and Fourier multipliers with singularities on certain sets
Let be a closed null set. We prove an equivalence between the Littlewood-Paley decomposition in with respect to the complementary intervals of and Fourier multipliers of Hörmander-Mihlin and Marcinkiewicz type with singularities on . Similar properties are studied in for a union of rays from the origin. Then there are connections with the maximal function operator with respect to all rectangles parallel to these rays. In particular, this maximal operator is proved to be bounded on , ,...
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