Strong Summability Of Fourier Series Research Articles

Pointwise (H, Φ) Strong Approximation by Fourier Series of LΨ Integrable Functions

We essentially extend and improve the classical result of G. H. Hardy and J. E. Littlewood on strong summability of Fourier series. We will present an estimation of the generalized strong mean (H, Φ) as an approximation version of the Totik type generaliza- tion of the result of G. H. Hardy, J. E. Littlewood, in case of integrable functions from LΨ. As a measure of such approximation we will use the function constructed by function Ψ com- plementary to Φ on the base of definition of the LΨ points. Some corollary and remarks will also be given.

Pointwise left( H,Phi right) Strong Approximation by Fourier Series of L^{1} Integrable Functions

We will present an estimation of the generalized strong mean left( H,Phi right) as an approximation version of the Totik type generalization of the results of J. Marcinkiewicz and A. Zygmund on strong summability of Fourier series of integrable functions. As a measure of such approximation we will use the function constructed by function Psi complementary to Phi on the base of definition of the Gabisoniya points. Some corollary and remark will also be given.

Strong summability of Fourier series and generalized Morrey spaces

We discuss some questions on strong summability of Fourier series in the context of periodic generalized Morrey spaces. By using periodic Lizorkin–Triebel–Morrey spaces as well as periodic Nikol’skij–Besov–Morrey spaces we are able to derive some if and only if assertions in this field. In addition we derive some conclusions on the local regularity of functions in terms of generalized Holder–Zygmund spaces. Finally, we characterize the asymptotic behaviour of the approximation numbers with respect to the identity mapping from periodic Nikol’skij–Besov–Morrey spaces into the space of continuous functions.

Strong summability of Fourier series and Morrey spaces

This work is dedicated to the investigation of strong summability of Fourier series in the context of periodic Morrey spaces. First, we study the Hilbert transform in the periodic vector-valued context. Boundedness of the Hilbert transform implies uniform estimates of the operator norms of the partial sums of the Fourier series. Afterwards, we study the Lizorkin-Triebel-Morrey and Nikol’skij-Besov-Morrey spaces. Here we concentrate on Lizorkin representations and embeddings into the scale of Holder-Zygmund spaces. In the final section, we study consequences for strong summability of Fourier series.

On Strong Summability of Fourier Series of Summable Functions

In the metric of L, we obtain estimates for the generalized means of deviations of partial Fourier sums from an arbitrary summable function in terms of the corresponding means of its best approximations by trigonometric polynomials.

Strong summability of fourier series of the periodic functions from H p (0<p≤1)

Exact estimates of the rate of approximation by the strong Riesz means are given, a new formula for theK-functional of the couple of spaces is found, two-sided estimates of approximation are proved.

Strong summability of orthogonal expansions of summable functions. I

We study the problem of strong summability of Fourier series in orthonormal systems of polynomial-type functions and establish local characteristics of the points of strong summability of series of this sort for summable functions. It is shown that the set of these points is a set of full measure in the region of uniform boundedness of systems under consideration.

Strong Summability of Fourier Series of the Periodic Functions from $H^p$ (0 $

Strong Summability of Fourier Series of the Periodic Functions from $H^p$ (0 $

Points of strong summability of fourier series

We study strong means of deviations of partial sums of expansions of functionsf in systems of functions of polynomial type.

Points of strong summability of Fourier series

The points of a function f e L at which there are given estimates of the rate of convergence to zero of the strong arithmetic means of its Fourier series and the trigonometrically conjugate series are characterized.

Strong summability of Fourier series of (gy, ?)-differentiable functions

Strong summability of Fourier series of (gy, ?)-differentiable functions

Strong summability of fourier series on classes of periodic functions

Strong summability of fourier series on classes of periodic functions

Characterizations of periodic function spaces of Besov-Sobolev type via approximation processes and relations to the strong summability of Fourier series

Characterizations of periodic function spaces of Besov-Sobolev type via approximation processes and relations to the strong summability of Fourier series

Strong summability of fourier series on classes of (?, ?)-differentiable functions

Strong summability of fourier series on classes of (?, ?)-differentiable functions

Strong summability of Fourier series

Strong summability of Fourier series

Points of strong summability of Fourier series

In this paper we present a new solution of Hardy and Littlewood's problem concerning strong summability of Fourier series; we also present a property of points of strong summability.

On strong summability of Fourier series. II

On strong summability of Fourier series. II

On a problem of strong summability of Fourier series

On a problem of strong summability of Fourier series

An Additional Note on the Strong Summability of Fourier Series

An Additional Note on the Strong Summability of Fourier Series

On the Strong Summability of Fourier Series

Journal of the London Mathematical SocietyVolume s1-33, Issue 3 p. 311-326 Notes and papers On the Strong Summability of Fourier Series T. M. Flett, T. M. Flett Department of Pure Mathematics, The University LiverpoolSearch for more papers by this author T. M. Flett, T. M. Flett Department of Pure Mathematics, The University LiverpoolSearch for more papers by this author First published: July 1958 https://doi.org/10.1112/jlms/s1-33.3.311AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volumes1-33, Issue3July 1958Pages 311-326 RelatedInformation