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## Open Mathematics

2012 | 10 | 6 | 2033-2050
Tytuł artykułu

### New Orlicz variants of Hardy type inequalities with power, power-logarithmic, and power-exponential weights

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
We obtain Hardy type inequalities $$\int_0^\infty {M\left( {\omega \left( r \right)\left| {u\left( r \right)} \right|} \right)\rho \left( r \right)dr} \leqslant C_1 \int_0^\infty {M\left( {\left| {u\left( r \right)} \right|} \right)\rho \left( r \right)dr + C_2 \int_0^\infty {M\left( {\left| {u'\left( r \right)} \right|} \right)\rho \left( r \right)dr,} }$$ and their Orlicz-norm counterparts $$\left\| {\omega u} \right\|_{L^M (\mathbb{R}_ + ,\rho )} \leqslant \tilde C_1 \left\| u \right\|_{L^M (\mathbb{R}_ + ,\rho )} + \tilde C_2 \left\| {u'} \right\|_{L^M (\mathbb{R}_ + ,\rho )} ,$$ with an N-function M, power, power-logarithmic and power-exponential weights ω, ρ, holding on suitable dilation invariant supersets of C 0∞(ℝ+). Maximal sets of admissible functions u are described. This paper is based on authors’ earlier abstract results and applies them to particular classes of weights.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
2033-2050
Opis fizyczny
Daty
wydano
2012-12-01
online
2012-10-12
Twórcy
autor
• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland
• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland
Bibliografia
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