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Discretization and antidiscretization of Lorentz norms with no restrictions on weights

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10441250" target="_blank" >RIV/00216208:11320/21:10441250 - isvavai.cz</a>

  • Alternative codes found

    RIV/68407700:21230/22:00359331

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZwUtOKtd7B" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZwUtOKtd7B</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s13163-021-00399-7" target="_blank" >10.1007/s13163-021-00399-7</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Discretization and antidiscretization of Lorentz norms with no restrictions on weights

  • Original language description

    We improve the discretization technique for weighted Lorentz norms by eliminating all “non-degeneracy” restrictions on the involved weights. We use the new method to provide equivalent estimates on the optimal constant C such that the inequality (∫0L(f∗(t))qw(t)dt)1q≤C(∫0L(∫0tu(s)ds)-p(∫0tf∗(s)u(s)ds)pv(t)dt)1pholds for all relevant measurable functions, where L∈ (0 , ∞] , p, q∈ (0 , ∞) and u, v, w are locally integrable weights, u being strictly positive. In the case of weights that would be otherwise excluded by the restrictions, it is shown that additional limit terms naturally appear in the characterizations of the optimal C. A weak analogue for p= ∞ is also presented.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

    Result was created during the realization of more than one project. More information in the Projects tab.

  • Continuities

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

Others

  • Publication year

    2021

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Revista Matematica Complutense

  • ISSN

    1139-1138

  • e-ISSN

  • Volume of the periodical

    2021

  • Issue of the periodical within the volume

    6

  • Country of publishing house

    ES - SPAIN

  • Number of pages

    34

  • Pages from-to

    1-34

  • UT code for WoS article

    000664410600001

  • EID of the result in the Scopus database

    2-s2.0-85108697143