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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Reduction theorems for discrete Hardy operator on monoton sequence cones (0<p<1)
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA23-04720S" target="_blank" >GA23-04720S: Fine properties of functions, operators and function spaces</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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