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Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces

100%

García-Cuerva J., Kazarian K. S.

Studia Mathematica

1994

tom 109

nr 3

255-276

We study sufficient conditions on the weight w, in terms of membership in the $A_p$ classes, for the spline wavelet systems to be unconditional bases of the weighted space $H^p(w)$. The main tool to obtain these results is a very simple theory of regular Calderón-Zygmund operators.

Integral operators and weighted amalgams

86%

Carton-Lebrun C., Heinig H. P., Hofmann S. C.

Studia Mathematica

1994

tom 109

nr 2

133-157

For large classes of indices, we characterize the weights u, v for which the Hardy operator is bounded from $ℓ^{q̅}(L^{p̅}_{v})$ into $ℓ^{q}(L^{p}_{u})$. For more general operators of Hardy type, norm inequalities are proved which extend to weighted amalgams known estimates in weighted $L^p$-spaces. Amalgams of the form $ℓ^{q}(L^{p}_{w})$, 1 < p,q < ∞ , q ≠ p, $w ∈ A_p$, are also considered and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator and local maximal operator in these spaces are obtained.

Ograniczanie wyników

2 Studia Mathematica

1 Carton-Lebrun C.

1 García-Cuerva J.

1 Heinig H. P.

1 Hofmann S. C.

1 Kazarian K. S.

2 1994

Wyniki wyszukiwania

Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces

Integral operators and weighted amalgams