Rearrangement estimates of the area integrals
We derive weighted rearrangement estimates for a large class of area integrals. The main approach used earlier to study these questions is based on distribution function inequalities.
Rearrangements of periodic multiplicative orthogonal series
Recent developments in the theory of function spaces with dominating mixed smoothness
The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation...
Recent developments in the theory of Haar series
Recent developments in the theory of Walsh series.
Recent progress on the Kakeya conjecture.
We survey recent developments on the Kakeya problem.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
Recent trends on analytic properties of matrix orthonormal polynomials.
Recognition and limit theorems for -multipliers
Reconstruction in time-warped weighted shift-invariant spaces with application to spline subspaces.
Reconstruction of functions from their triple correlations.
Recovery of band-limited functions on locally compact Abelian groups from irregular samples
Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group . The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek’s work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative...
Rectifiabilité quantifié et le problème du voyageur de commerce
Rectifiability, analytic capacity, and singular integrals.
Recurrence for cosine series with bounded gaps
Ullrich, Grubb and Moore proved that a lacunary trigonometric series satisfying Hadamard's gap condition is recurrent a.e. We prove the existence of a recurrent trigonometric series with bounded gaps.
Recurrence relations for orthogonal polynomials on algebraic curves
Recurrence relations for the coefficients of expansions in classical orthogonal polynomials of a discrete variable
A method is given to find a recurrence relation for the coefficients of the series expansion of a function f with respect to classical orthogonal polynomials of a discrete variable, which follows from a linear difference equation satisfied by f.
Recurrence relations with periodic coefficients and Chebyshev polynomials
We show that polynomials defined by recurrence relations with periodic coefficients may be represented with the help of Chebyshev polynomials of the second kind.
Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials
Let be any sequence of classical orthogonal polynomials. Further, let f be a function satisfying a linear differential equation with polynomial coefficients. We give an algorithm to construct, in a compact form, a recurrence relation satisfied by the coefficients in . A systematic use of the basic properties (including some nonstandard ones) of the polynomials results in obtaining a low order of the recurrence.
Refined Hardy inequalities
The aim of this article is to present “refined” Hardy-type inequalities. Those inequalities are generalisations of the usual Hardy inequalities, their additional feature being that they are invariant under oscillations: when applied to highly oscillatory functions, both sides of the refined inequality are of the same order of magnitude. The proof relies on paradifferential calculus and Besov spaces. It is also adapted to the case of the Heisenberg group.
Refinement equations for generalized translations.