A study of some constants characterizing the weighted Hardy inequality

• Autorzy: Alois Kufner , Lars-Erik Persson , Anna Wedestig
• Języki publikacji: EN

Abstrakty

EN

The modern form of Hardy's inequality means that we have a necessary and sufficient condition on the weights u and v on [0,b] so that the mapping <br> $H: L^{p}(0,b;v) → L^{q}(0,b;u)$ <br> is continuous, where $Hf(x) = ∫_{0}^{x} f(t)dt$ is the Hardy operator. We consider the case 1 < p ≤ q < ∞ and then this condition is usually written in the Muckenhoupt form <br> (*) $A₁: = sup_{0<x<b}A_{M}(x) < ∞$. <br> In this paper we discuss and compare some old and new other constants $A_{i}$ of the form (*), which also characterize Hardy's inequality. We also point out some dual forms of these characterizations, prove some new compactness results and state some open problems.

Kategorie tematyczne

• 26D15: Inequalities for sums, series and integrals
• 47B38: Operators on function spaces (general)
• 47B07: Operators defined by compactness properties
• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2004
• Tom: 64
• Numer: 1
• Strony: 135-146

Daty

wydano

2004

Twórcy

autor

Alois Kufner

• Matematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

autor

Lars-Erik Persson

• Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden

autor

Anna Wedestig

• Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden

Identyfikatory

DOI

10.4064/bc64-0-11