# 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

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topCarton-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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