Boundedness of Hardy-type operators with a kernel: integral weighted conditions for the case

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10372631" target="_blank" >RIV/00216208:11320/17:10372631 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/s13163-017-0230-9" target="_blank" >http://dx.doi.org/10.1007/s13163-017-0230-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s13163-017-0230-9" target="_blank" >10.1007/s13163-017-0230-9</a>

Result language

angličtina

Original language name

Boundedness of Hardy-type operators with a kernel: integral weighted conditions for the case

Original language description

Let 1 &lt; p &lt; infinity and 0 &lt; q &lt; p. We prove necessary and sufficient conditions under which the weighted inequality (integral(infinity)(0) (integral(t)(0) f(x)U(x, t) dx)(q) w(t) dt)(1/q) &lt;= C (integral(infinity)(0) f(p)(t)v(t) dt)(1/p), where U is a so-called -regular kernel, holds for all nonnegative measurable functions f on (0, infinity). The conditions have an explicit integral form. Analogous results for the case and for the dual version of the inequality are also presented. The results are applied to close various gaps in the theory of weighted operator inequalities.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2017

Confidentiality

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

Name of the periodical

Revista Matematica Complutense

ISSN

1139-1138

e-ISSN

—

Volume of the periodical

30

Issue of the periodical within the volume

3

Country of publishing house

ES - SPAIN

Number of pages

41

Pages from-to

547-587

UT code for WoS article

000408650000007

EID of the result in the Scopus database

2-s2.0-85017416303