Optimal estimates for the fractional Hardyoperator

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F15%3A00242128" target="_blank" >RIV/68407700:21110/15:00242128 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.4064/sm227-1-1" target="_blank" >http://dx.doi.org/10.4064/sm227-1-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4064/sm227-1-1" target="_blank" >10.4064/sm227-1-1</a>

Result language

angličtina

Original language name

Optimal estimates for the fractional Hardyoperator

Original language description

Let A(alpha) f(x) = vertical bar B(0, vertical bar x vertical bar)vertical bar(-alpha/n) integral(B(0,vertical bar x vertical bar)) f(t)dt be the n-dimensional fractional Hardy operator, where 0 < alpha <= n. It is well-known that A(alpha) is bounded from L-p to L-p alpha with p(alpha) = np/(alpha p - np + n) when n (1 - 1/p) < alpha <= n. We improve this result within the framework of Banach function spaces, for instance, weighted Lebesgue spaces and Lorentz spaces. We in fact find a 'source' space S-alpha,S-Y, which is strictly larger than X, and a 'target' space T-Y, which is strictly smaller than Y, under the assumption that A(alpha) is bounded from X into Y and the Hardy-Littlewood maximal operator M is bounded from Y into Y, and prove that A(alpha) is bounded from S-alpha,S-Y into T-Y. We prove optimality results for the action of A(alpha) and the associate operator A(alpha)' on such spaces, as an extension of the results of Mizuta et al. (2013) and Nekvinda and Pick (2011). We a

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F08%2F0383" target="_blank" >GA201/08/0383: Function Spaces, Weighted Inequalities and Interpolation</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2015

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Studia Mathematica

ISSN

0039-3223

e-ISSN

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Volume of the periodical

227

Issue of the periodical within the volume

1

Country of publishing house

PL - POLAND

Number of pages

19

Pages from-to

1-19

UT code for WoS article

000365157600001

EID of the result in the Scopus database

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