### Characterization of a two-weighted vector-valued inequality for fractional maximal operators.

Rakotondratsimba, Y. (1998)

Georgian Mathematical Journal

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Rakotondratsimba, Y. (1998)

Georgian Mathematical Journal

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Shiying Zhao (1996)

Colloquium Mathematicae

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In this paper, we discuss a class of weighted inequalities for operators of potential type on homogeneous spaces. We give sufficient conditions for the weak and strong type weighted inequalities sup_{λ>0} λ|{x ∈ X : |T(fdσ)(x)|>λ }|_{ω}^{1/q} ≤ C (∫_{X} |f|^{p}dσ)^{1/p} and (∫_{X} |T(fdσ)|^{q}dω )^{1/q} ≤ C (∫_X |f|^{p}dσ )^{1/p} in the cases of 0 < q < p ≤ ∞ and 1 ≤ q < p < ∞, respectively, where T is an operator of potential type, and ω and σ are Borel measures on...

Rakotondratsimba, Y. (1998)

Georgian Mathematical Journal

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Genebashvili, I., Gogatishvili, A., Kokilashvili, V. (1996)

Georgian Mathematical Journal

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Edmunds, D.E., Kokilashvili, V., Meskhi, A. (2001)

Georgian Mathematical Journal

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Gogatishvili, A., Kokilashvili, V. (1996)

Georgian Mathematical Journal

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Meskhi, A. (1998)

Georgian Mathematical Journal

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K. Rauf, C. O. Imoru (2002)

Kragujevac Journal of Mathematics

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Cavalheiro, A.C. (2008)

Acta Mathematica Universitatis Comenianae. New Series

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Liu, Lanzhe (2004)

Documenta Mathematica

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Kokilashvili, V., Meskhi, A. (2001)

Georgian Mathematical Journal

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Marek Ptak (1995)

Annales Polonici Mathematici

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We present a model for two doubly commuting operator weighted shifts. We also investigate general pairs of operator weighted shifts. The above model generalizes the model for two doubly commuting shifts. WOT-closed algebras for such pairs are described. We also deal with reflexivity for such pairs assuming invertibility of operator weights and a condition on the joint point spectrum.

Kokilashvili, V., Meskhi, A. (1999)

Georgian Mathematical Journal

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