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Weighted Hardy inequalities and Hardy transforms of weights

100%

Cerdà J., Martín J.

Studia Mathematica

2000

tom 139

nr 2

189-196

Many problems in analysis are described as weighted norm inequalities that have given rise to different classes of weights, such as $A_p$-weights of Muckenhoupt and $B_p$-weights of Ariño and Muckenhoupt. Our purpose is to show that different classes of weights are related by means of composition with classical transforms. A typical example is the family $M_p$ of weights w for which the Hardy transform is $L_p(w)$-bounded. A $B_p$-weight is precisely one for which its Hardy transform is in $M_p$, and also a weight whose indefinite integral is in $A_{p+1}$

Interpolation of quasicontinuous functions

81%

Cerdà J., Martín J., Silvestre P.

Banach Center Publications

2011

tom 95

nr 1

281-286

If C is a capacity on a measurable space, we prove that the restriction of the K-functional $K(t,f;L^p(C),L^∞(C))$ to quasicontinuous functions f ∈ QC is equivalent to $K(t,f;L^p(C) ∩ QC, L^∞(C) ∩ QC)$. We apply this result to identify the interpolation space $(L^{p₀,q₀}(C) ∩ QC,L^{p₁,q₁}(C) ∩ QC)_{θ,q}$.

Ograniczanie wyników

1 Banach Center Publications

1 Studia Mathematica

2 Cerdà J.

2 Martín J.

1 Silvestre P.

1 2011

1 2000

Wyniki wyszukiwania

Weighted Hardy inequalities and Hardy transforms of weights

Interpolation of quasicontinuous functions