Reduction theorems for discrete Hardy operator on monoton sequence cones (0<p<1)

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00644223" target="_blank" >RIV/67985840:_____/25:00644223 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.26577/JMMCS202512842" target="_blank" >https://doi.org/10.26577/JMMCS202512842</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.26577/JMMCS202512842" target="_blank" >10.26577/JMMCS202512842</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Reduction theorems for discrete Hardy operator on monoton sequence cones (0<p<1)

Popis výsledku v původním jazyce

In this paper, we consider the discrete Hardy and Copson operators on the cone of nonnegative monotone sequences. We prove that weighted inequalities of the form lp→ lq for discrete Hardy and Copson operators on the cone of monotone sequences, in the case 0 < q < ∞, 0<p<1, can be reduced to the corresponding inequalities on the cone of nonnegative sequences. The latter possess a broader basis for proof, which significantly extends the possibilities for their analysis. Weighted inequalities for the integral Hardy operator (in the continuous setting) on the cone of nonnegative nonincreasing functions have been studied previously by many authors. Reduction theorems for inequalities involving Hardy-type integral operators on the cone of nonincreasing functions to inequalities on the cone of nonnegative functions are also well known. We present various theorems concerning the equivalence of inequalities for discrete Hardy and Copson operators on the cone of nonnegative nonincreasing sequences and inequalities on the cone of nonnegative sequences. Our proofs differ substantially from those in the continuous case. Methods applicable in the continuous setting do not always work in the discrete setting. For the case p>1, analogous results were obtained by the authors earlier.

Název v anglickém jazyce

Reduction theorems for discrete Hardy operator on monoton sequence cones (0<p<1)

Popis výsledku anglicky

In this paper, we consider the discrete Hardy and Copson operators on the cone of nonnegative monotone sequences. We prove that weighted inequalities of the form lp→ lq for discrete Hardy and Copson operators on the cone of monotone sequences, in the case 0 < q < ∞, 0<p<1, can be reduced to the corresponding inequalities on the cone of nonnegative sequences. The latter possess a broader basis for proof, which significantly extends the possibilities for their analysis. Weighted inequalities for the integral Hardy operator (in the continuous setting) on the cone of nonnegative nonincreasing functions have been studied previously by many authors. Reduction theorems for inequalities involving Hardy-type integral operators on the cone of nonincreasing functions to inequalities on the cone of nonnegative functions are also well known. We present various theorems concerning the equivalence of inequalities for discrete Hardy and Copson operators on the cone of nonnegative nonincreasing sequences and inequalities on the cone of nonnegative sequences. Our proofs differ substantially from those in the continuous case. Methods applicable in the continuous setting do not always work in the discrete setting. For the case p>1, analogous results were obtained by the authors earlier.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA23-04720S" target="_blank" >GA23-04720S: Jemné vlastnosti funkcí, operátorů a prostorů funkcí</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematics Mechanics and Computer Science

ISSN

1563-0277

e-ISSN

2617-4871

Svazek periodika

128

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

KZ - Republika Kazachstán

Počet stran výsledku

13

Strana od-do

12-24

Kód UT WoS článku

001652556400002

EID výsledku v databázi Scopus

2-s2.0-105027246559