On boundedness of weighted Hardy operator in \(L^{p(\cdot)}\) and regularity condition

DOI10.1155/2010/837951zbMath1211.47065OpenAlexW2079200173WikidataQ59253399 ScholiaQ59253399MaRDI QIDQ623644

Aziz Harman, Farman I. Mamedov

Publication date: 8 February 2011

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/225490

zbMATH Keywords

variable exponent Lebesgue spacesHardy type weighted inequality

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Linear operators on function spaces (general) (47B38) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (9)

Hardy's inequality on Hardy-Morrey spaces with variable exponents ⋮ On a general weighted Hardy type inequality in the variable exponent Lebesgue spaces ⋮ On necessary condition for the variable exponent Hardy inequality ⋮ A new approach for weighted Hardy's operator in VELS ⋮ Weighted Hardy-type inequalities in variable exponent Morrey-type spaces ⋮ A necessary and sufficient condition for Hardy's operator in the variable Lebesgue space ⋮ Compactness for the weighted Hardy operator in variable exponent spaces ⋮ A necessary and sufficient condition for Hardy's operator in ⋮ The Calderón operator and the Stieltjes transform on variable Lebesgue spaces with weights

Cites Work

• On a Hardy type general weighted inequality in spaces \(L ^{p(\cdot )}\)
• On a weighted inequality of Hardy type in spaces \(L^{p(\cdot)}\)
• An example of a space of \(L^{p(x)}\) on which the Hardy-Littlewood maximal operator is not bounded
• Hardy's inequality in power-type weighted \(L^{p(\cdot)}(0,\infty )\) spaces
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• A class of De Giorgi type and Hölder continuity
• On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators
• Regularity results for a class of functionals with non-standard growth

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