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Convolution operators on Hardy spaces

Chin-Cheng Lin (1996)

Studia Mathematica

We give sufficient conditions on the kernel K for the convolution operator Tf = K ∗ f to be bounded on Hardy spaces H p ( G ) , where G is a homogeneous group.

Convolution operators with anisotropically homogeneous measures on 2 n with n-dimensional support

E. Ferreyra, T. Godoy, M. Urciuolo (2002)

Colloquium Mathematicae

Let α i , β i > 0 , 1 ≤ i ≤ n, and for t > 0 and x = (x₁,...,xₙ) ∈ ℝⁿ, let t x = ( t α x , . . . , t α x ) , t x = ( t β x , . . . , t β x ) and | | x | | = i = 1 n | x i | 1 / α i . Let φ₁,...,φₙ be real functions in C ( - 0 ) such that φ = (φ₁,..., φₙ) satisfies φ(t • x) = t ∘ φ(x). Let γ > 0 and let μ be the Borel measure on 2 n given by μ ( E ) = χ E ( x , φ ( x ) ) | | x | | γ - α d x , where α = i = 1 n α i and dx denotes the Lebesgue measure on ℝⁿ. Let T μ f = μ f and let | | T μ | | p , q be the operator norm of T μ from L p ( 2 n ) into L q ( 2 n ) , where the L p spaces are taken with respect to the Lebesgue measure. The type set E μ is defined by E μ = ( 1 / p , 1 / q ) : | | T μ | | p , q < , 1 p , q . In the case α i β k for 1 ≤ i,k ≤ n we characterize the type set under...

Corrigenda: On the product theory of singular integrals.

Alexander Nagel, Elias M. Stein (2005)

Revista Matemática Iberoamericana

We wish to acknowledge and correct an error in a proof in our paper On the product theory of singular integrals, which appeared in Revista Matemática Iberoamericana, volume 20, number 2, 2004, pages 531-561.

Courbes corde-arc et espaces de Hardy généralisés

Guy David (1982)

Annales de l'institut Fourier

Étant donné Γ une courbe de Jordan rectifiable du plan complexe admettant le paramétrage par la longueur d’arc z ( s ) , on étudie les relations entre la géométrie de Γ et la position dans L 2 ( Γ ) des deux espaces de Hardy associés à Γ . Plus précisément, on montre que si L 2 ( Γ ) est la somme presque-orthogonale des espaces de Hardy, la courbe Γ satisfait à une condition de type corde-arc, c’est-à-dire que pour tout s et tout t de R , | s - t | C | z ( s ) - z ( t ) | . Ce résultat est une sorte de réciproque à la généralisation du théorème de Calderón...

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