Displaying similar documents to “On weak restricted estimates and endpoints problems for convolutions with oscillating kernels (II)”

Weak type radial convolution operators on free groups

Tadeusz Pytlik, Ryszard Szwarc (2008)

Studia Mathematica

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Radial convolution operators on free groups with nonnegative kernel of weak type (2,2) and of restricted weak type (2,2) are characterized. Estimates of weak type (p,p) are obtained as well for 1 < p < 2.

Para-accretive functions, the weak boundedness property and the Tb theorem.

Yongsheng Han, Eric T. Sawyer (1990)

Revista Matemática Iberoamericana

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G. David, J.-L. Journé and S. Semmes have shown that if b and b are para-accretive functions on R, then the Tb theorem holds: A linear operator T with Calderón-Zygmund kernel is bounded on L if and only if Tb ∈ BMO, T*b ∈ BMO and MTM has the weak boundedness property. Conversely they showed that when b = b = b, para-accretivity of b is necessary for Tb Theorem to hold. In this paper we show that para-accretivity of both b and b is necessary for the Tb Theorem to hold in general. In addition,...

Weak* properties of weighted convolution algebras II

Sandy Grabiner (2010)

Studia Mathematica

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We show that if ϕ is a continuous homomorphism between weighted convolution algebras on ℝ⁺, then its extension to the corresponding measure algebras is always weak* continuous. A key step in the proof is showing that our earlier result that normalized powers of functions in a convolution algebra on ℝ⁺ go to zero weak* is also true for most measures in the corresponding measure algebra. For some algebras, we can determine precisely which measures have normalized powers converging to zero...

A weak molecule condition for certain Triebel-Lizorkin spaces

Steve Hofmann (1992)

Studia Mathematica

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A weak molecule condition is given for the Triebel-Lizorkin spaces Ḟ_p^{α,q}, with 0 < α < 1 and 1 < p, q < ∞. As an easy corollary, one may deduce, by atomic-molecular methods, a Triebel-Lizorkin space "T1" Theorem of Han and Sawyer, and Han, Jawerth, Taibleson and Weiss, for Calderón-Zygmund kernels K(x,y) which are not assumed to satisfy any regularity condition in the y variable.