Sharp Estimates for Lebesgue Constants

Sharp Estimates of the Embedding Constants for Besov Spaces

Sharp estimates are obtained for the rates of blow up of the norms of embeddings of Besov spaces in Lorentz spaces as the parameters approach critical values.

Sharp Bounds for Lebesgue Constants of Barycentric Rational Interpolation at Equidistant Points

Lebesgue constants for the weak greedy algorithm

We estimate the Lebesgue constants for the weak thresholding greedy algorithm in a Banach space relative to a biorthogonal system. The estimates involve the weakness (relaxation) parameter of the algorithm, as well as properties of the basis, such as its quasi-greedy constant and democracy function.

Lebesgue Constants and Fourier Transform

This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function generating such a method. Only few proofs are given in order to illustrate a general idea of techniques applied. Among the results are well known elsewhere as well a...

Estimates for the constants of Landau and Lebesgue via some inequalities for the Wallis ratio

We establish several new inequalities of the constants of Landau and Lebesgue