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

Agnieszka Kałamajska; Katarzyna Pietruska-Pałuba

Agnieszka Kałamajska ; Katarzyna Pietruska-Pałuba

Open Mathematics, Tome 10 (2012), p. 2033-2050 / Harvested from The Polish Digital Mathematics Library

Résumé

We obtain Hardy type inequalities $\int_{0}^{\infty} M (ω (r) |u (r)|) ρ (r) d r ⩽ C_{1} \int_{0}^{\infty} M (|u (r)|) ρ (r) d r + C_{2} \int_{0}^{\infty} M (|u^{'} (r)|) ρ (r) d r,$ and their Orlicz-norm counterparts ${∥ω u∥}_{L^{M} (ℝ_{+}, ρ)} ⩽ {\tilde{C}}_{1} {∥u∥}_{L^{M} (ℝ_{+}, ρ)} + {\tilde{C}}_{2} {∥u^{'}∥}_{L^{M} (ℝ_{+}, ρ)},$ 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.

Publié le : 2012-01-01

Zbl 1260.26018

EUDML-ID : urn:eudml:doc:268960

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     author = {Agnieszka Ka\l amajska and Katarzyna Pietruska-Pa\l uba},
     title = {New Orlicz variants of Hardy type inequalities with power, power-logarithmic, and power-exponential weights},
     journal = {Open Mathematics},
     volume = {10},
     year = {2012},
     pages = {2033-2050},
     zbl = {1260.26018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0116-5}
}

Agnieszka Kałamajska; Katarzyna Pietruska-Pałuba. New Orlicz variants of Hardy type inequalities with power, power-logarithmic, and power-exponential weights. Open Mathematics, Tome 10 (2012) pp. 2033-2050. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0116-5/

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