Displaying similar documents to “On Littlewood-Paley functions”

Hardy space estimates for multilinear operators (II).

Loukas Grafakos (1992)

Revista Matemática Iberoamericana

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We continue the study of multilinear operators given by products of finite vectors of Calderón-Zygmund operators. We determine the set of all r ≤ 1 for which these operators map products of Lebesgue spaces L(R) into the Hardy spaces H(R). At the endpoint case r = n/(n + m + 1), where m is the highest vanishing moment of the multilinear operator, we prove a weak type result.

A class of Fourier multipliers on H¹(ℝ²)

Michał Wojciechowski (2000)

Studia Mathematica

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An integral criterion for being an H 1 ( ℝ 2 ) Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.

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 - ∞ ∞ 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 ∈ L ∞ (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.