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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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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.
Twórcy
  • Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland, kalamajs@mimuw.edu.pl
  • Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland, kpp@mimuw.edu.pl
Bibliografia
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-012-0116-5
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