Kernel estimates for fractional integrals with polynomial weights

Jan-Olov Strömberg; Richard Wheeden

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Multilinear singular integrals involving a derivative of fractional order

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A note on fractional integration

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Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces.

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On molecules and fractional integrals on spaces of homogeneous type with finite measure

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In this paper we prove the continuity of fractional integrals acting on nonhomogeneous function spaces defined on spaces of homogeneous type with finite measure. A definition of the molecules which are used in the $H^{p}$ theory is given. Results are proved for $L^{p}$ , $H^{p}$ , BMO, and Lipschitz spaces.

Virtually repelling fixed point.

Xavier Buff (2003)

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In this article, we study the notion oí virtually repelling fixed point. We first give a definition and an interpretation of it. We then prove that most proper holomorphic mappings f: U -> V with U contained in V have at least one virtually repelling fixed point.

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Fractional integration on the space $H^{1}$ and its dual

Umberto Neri (1975)

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Norm inequalities for potential-type operators.

Sagun Chanillo, Jan-Olov Strömberg, Richard L. Wheeden (1987)

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The purpose of this paper is to derive norm inequalities for potentials of the form Tf(x) = ∫_(Rⁿ) f(y)K(x,y)dy, x ∈ Rⁿ, when K is a Kernel which satisfies estimates like those that hold for the Green function associated with the degenerate elliptic equations studied in [3] and [4].

$L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains

Yibiao Pan, Gary Sampson, Paweł Szeptycki (1997)

Studia Mathematica

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We prove the $L^{p}$ boundedness of certain nonconvolutional oscillatory integral operators and give explicit description of their extended domains. The class of phase functions considered here includes the function ${| x |}^{α} {| y |}^{β}$ . Sharp boundedness results are obtained in terms of α, β, and rate of decay of the kernel at infinity.