2004
DOI: 10.4064/sm161-1-5
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Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces

Abstract: 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 ex… Show more

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Cited by 4 publications
(3 citation statements)
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“…At this point we would also like to note that Fefferman and Stein noted in [11] that w ∈ A 1 is a necessary condition for this inequality to hold. Since those works, the theory of weights and more in particular Fefferman-Stein inequalities and related variants have been studied in a variety of contexts [23,36,2,27] and for singular integrals [8,24,28,10,5,16] and their commutators [25,26,15]. See also [17,3,7].…”
Section: Intoduction and Main Resultsmentioning
confidence: 99%
“…At this point we would also like to note that Fefferman and Stein noted in [11] that w ∈ A 1 is a necessary condition for this inequality to hold. Since those works, the theory of weights and more in particular Fefferman-Stein inequalities and related variants have been studied in a variety of contexts [23,36,2,27] and for singular integrals [8,24,28,10,5,16] and their commutators [25,26,15]. See also [17,3,7].…”
Section: Intoduction and Main Resultsmentioning
confidence: 99%
“…In this section, we will follow some definitions from Tozoni. 16 We are going to discuss Banach-valued extensions of operators for functions defined on a homogeneous type space X and with values in a UMD Banach lattice.…”
Section: More On Singular Integralsmentioning
confidence: 99%
“…The theory of Banach-valued function spaces and integral operators in the context of UMD property was intensively studied in other studies. [6][7][8][9][10][11][12][13][14][15][16] For scalar functions grand Lebesgue spaces, L p) were introduced by Iwaniec and Sbordone in 1992. 17 The theory of Iwaniec-Sbordone space is nowadays one of intensively developing directions in modern analysis.…”
Section: Introductionmentioning
confidence: 99%