In this paper we investigate the degree of approximation of a function belonging to the generalized Zygmund class [Formula: see text] ([Formula: see text]) by Hausdorff means of its Fourier series. We also deduce a corollary and mention a few applications of our main results.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5420006 | PMC |
| http://dx.doi.org/10.1186/s13660-017-1361-8 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces.
Calc Var Partial Differ Equ
July 2024
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, TS Italy.
We revisit Yudovich's well-posedness result for the 2-dimensional Euler equations for an inviscid incompressible fluid on either a sufficiently regular (not necessarily bounded) open set or on the torus . We construct global-in-time weak solutions with vorticity in and in , where and are suitable uniformly-localized versions of the Lebesgue space and of the Yudovich space respectively, with no condition at infinity for the growth function . We also provide an explicit modulus of continuity for the velocity depending on the growth function .
View Article and Find Full Text PDFOn MV-Algebraic Versions of the Strong Law of Large Numbers.
Entropy (Basel)
July 2019
Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland.
Many-valued (MV; the many-valued logics considered by Łukasiewicz)-algebras are algebraic systems that generalize Boolean algebras. The MV-algebraic probability theory involves the notions of the state and observable, which abstract the probability measure and the random variable, both considered in the Kolmogorov probability theory. Within the MV-algebraic probability theory, many important theorems (such as various versions of the central limit theorem or the individual ergodic theorem) have been recently studied and proven.
View Article and Find Full Text PDFSufficient and necessary conditions of complete convergence for asymptotically negatively associated random variables.
J Inequal Appl
November 2018
1College of Mathematics and Statistics, Hengyang Normal University, Hengyang, P.R. China.
In this investigation, some sufficient and necessary conditions of the complete convergence for weighted sums of asymptotically negatively associated (ANA, in short) random variables are presented without the assumption of identical distribution. As an application of the main results, the Marcinkiewicz-Zygmund type strong law of large numbers based on weighted sums of ANA cases is obtained. The results of this paper extend and generalize some well-known corresponding ones.
View Article and Find Full Text PDFApproximation of functions in the generalized Zygmund class using Hausdorff means.
J Inequal Appl
May 2017
Department of Mathematics, Indiana University, Bloomington, IN 47405-7106 USA.
In this paper we investigate the degree of approximation of a function belonging to the generalized Zygmund class [Formula: see text] ([Formula: see text]) by Hausdorff means of its Fourier series. We also deduce a corollary and mention a few applications of our main results.
View Article and Find Full Text PDFWeighted norm inequalities for multilinear Calderón-Zygmund operators in generalized Morrey spaces.
J Inequal Appl
February 2017
Department of Mathematics, China University of Mining and Technology, Beijing, 100083 P.R. China.
In this paper, the authors study the boundedness of multilinear Calderón-Zygmund singular integral operators and their commutators in generalized Morrey spaces.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!