Integral operators and weighted amalgams

C. Carton-Lebrun; H. Heinig; S. Hofmann

Studia Mathematica (1994)

  • Volume: 109, Issue: 2, page 133-157
  • ISSN: 0039-3223

Abstract

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For large classes of indices, we characterize the weights u, v for which the Hardy operator is bounded from q ̅ ( L v p ̅ ) into q ( L u p ) . 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 q ( L w p ) , 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.

How to cite

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Carton-Lebrun, C., Heinig, H., and Hofmann, S.. "Integral operators and weighted amalgams." Studia Mathematica 109.2 (1994): 133-157. <http://eudml.org/doc/216065>.

@article{Carton1994,
abstract = {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.},
author = {Carton-Lebrun, C., Heinig, H., Hofmann, S.},
journal = {Studia Mathematica},
keywords = {amalgam spaces; weights; $A_p$ weights; Hardy operator; Hardy-Littlewood maximal operator; weighted amalgam inequalities; integral operators; weighted amalgam spaces},
language = {eng},
number = {2},
pages = {133-157},
title = {Integral operators and weighted amalgams},
url = {http://eudml.org/doc/216065},
volume = {109},
year = {1994},
}

TY - JOUR
AU - Carton-Lebrun, C.
AU - Heinig, H.
AU - Hofmann, S.
TI - Integral operators and weighted amalgams
JO - Studia Mathematica
PY - 1994
VL - 109
IS - 2
SP - 133
EP - 157
AB - 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.
LA - eng
KW - amalgam spaces; weights; $A_p$ weights; Hardy operator; Hardy-Littlewood maximal operator; weighted amalgam inequalities; integral operators; weighted amalgam spaces
UR - http://eudml.org/doc/216065
ER -

References

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