Singular Integral Operators with Operator-Valued Kernels on Spaces of Homogeneous Type

Bordin, Benjamin; Fernandes, Dicesar Lass

doi:10.4171/zaa/617

Z. Anal. Anwend.

1992

DOI: 10.4171/zaa/617

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Singular Integral Operators with Operator-Valued Kernels on Spaces of Homogeneous Type

Benjamin Bordin¹,

Dicesar Lass Fernandes²

Abstract: We give a generalized form of the Hormander-Schwartz-Triebel theorem for singular integral operators of potential type as well as a sequentiaI version. Applications include fractionary maximal inequalities of Hardy- Littlewood and Fefferman-Stein type.

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2004

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“…For W = 1 and E = q , 1 < q < ∞, but for more general spaces X (of homogeneous type) it was proved in [2,22]. Theorem 1.3 for X = R n and W = 1 was proved in [21].…”

mentioning

confidence: 95%

Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces

Tozoni

2004

Studia Math.

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Abstract. Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis (We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient conditions on the kernel of a singular integral operator to have the boundedness of the vector-valued extension of this operator on L p (X, W dµ; E) for 1 < p < ∞ and for a weight W in the Muckenhoupt class A p (X). Applications to singular integral operators on the unit sphere S n and on a finite product of local fields K n are given. The versions of all these results for vector-valued extensions of operators on functions defined on a homogeneous space X and with values in a UMD Banach lattice are also given.

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“…For W = 1 and E = q , 1 < q < ∞, but for more general spaces X (of homogeneous type) it was proved in [2,22]. Theorem 1.3 for X = R n and W = 1 was proved in [21].…”

mentioning

confidence: 95%

Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces

Tozoni

2004

Studia Math.

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show abstract

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Singular Integral Operators with Operator-Valued Kernels on Spaces of Homogeneous Type

Abstract: We give a generalized form of the Hormander-Schwartz-Triebel theorem for singular integral operators of potential type as well as a sequentiaI version. Applications include fractionary maximal inequalities of Hardy- Littlewood and Fefferman-Stein type.

Cited by 1 publication

References 0 publications

Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces

Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces

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