Optimal estimates for the fractional Hardyoperator

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Optimal estimates for the fractional Hardyoperator

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

Optimal estimates for the fractional Hardyoperator

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F08%2F0383" target="_blank" >GA201/08/0383: Prostory funkcí, váhové nerovnosti a interpolace</a><br>

Návaznosti

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

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Studia Mathematica

ISSN

0039-3223

e-ISSN

—

Svazek periodika

227

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

19

Strana od-do

1-19

Kód UT WoS článku

000365157600001

EID výsledku v databázi Scopus

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