On a singular integral

Calixto Calderón

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Weighted two-parameter Bergman space inequalities.

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A covering lemma with applications to differentiability of measures and singular integral operators

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A variant sharp estimate for multilinear singular integral operators

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We establish a variant sharp estimate for multilinear singular integral operators. As applications, we obtain the weighted norm inequalities on general weights and certain $L l o g^{+} L$ type estimates for these multilinear operators.

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Weighted weak type (1,1) estimates for oscillatory singular integrals

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We consider the $A_{1}$ -weights and prove the weighted weak type (1,1) inequalities for certain oscillatory singular integrals.

Nonconvolution transforms with oscillating kernels that map $Ḃ_{1}^{0, 1}$ into itself

G. Sampson (1993)

Studia Mathematica

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We consider operators of the form $(Ω f) (y) = ʃ_{- \infty}^{\infty} Ω (y, u) f (u) d u$ with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and $h \in L^{\infty}$ (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space $Ḃ_{1}^{0, 1}$ (= B) into itself. In particular, all operators with $h (y) = e^{{i | y |}^{a}}$ , a > 0, a ≠ 1, map B into itself.

BMO and smooth truncation in Sobolev spaces

David Adams, Michael Frazier (1988)

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