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Displaying similar documents to “Radial convolutors on free groups”

An exponential estimate for convolution powers

Roger Jones (1999)

Studia Mathematica

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We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.

Several characterizations for the special atom spaces with applications.

Geraldo Soares de Souza, Richard O'Neil, Gary Sampson (1986)

Revista Matemática Iberoamericana

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The theory of functions plays an important role in harmonic analysis. Because of this, it turns out that some spaces of analytic functions have been studied extensively, such as H-spaces, Bergman spaces, etc. One of the major insights that has developed in the study of H-spaces is what we call the real atomic characterization of these spaces.

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.

On the characterization of Hardy-Besov spaces on the dyadic group and its applications

Jun Tateoka (1994)

Studia Mathematica

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C. Watari [12] obtained a simple characterization of Lipschitz classes L i p ( p ) α ( W ) ( 1 ≥ p ≥ ∞ , α > 0 ) on the dyadic group using the L p -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces B p , q α on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces B p , q α by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality...