Weight inequalities for singular integrals defined on spaces of homogeneous and nonhomogeneous type.

Edmunds, D.E.; Kokilashvili, V.; Meskhi, A.

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Solution of some weight problems for the Riemann-Liouville and Weyl operators.

Meskhi, A. (1998)

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On boundedness of a certain class of Hardy-Steklov type operators in Lebesgue spaces.

Stepanov, V.D., Ushakova, E.P. (2010)

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On weighted inequalities for operators of potential type

Shiying Zhao (1996)

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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...