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We give sufficient conditions on the kernel K for the convolution operator Tf = K ∗ f to be bounded on Hardy spaces , where G is a homogeneous group.
Let , 1 ≤ i ≤ n, and for t > 0 and x = (x₁,...,xₙ) ∈ ℝⁿ, let , and . Let φ₁,...,φₙ be real functions in such that φ = (φ₁,..., φₙ) satisfies φ(t • x) = t ∘ φ(x). Let γ > 0 and let μ be the Borel measure on given by
,
where and dx denotes the Lebesgue measure on ℝⁿ. Let and let be the operator norm of from into , where the spaces are taken with respect to the Lebesgue measure. The type set is defined by
.
In the case for 1 ≤ i,k ≤ n we characterize the type set under...
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.
Étant donné une courbe de Jordan rectifiable du plan complexe admettant le paramétrage par la longueur d’arc , on étudie les relations entre la géométrie de et la position dans des deux espaces de Hardy associés à . Plus précisément, on montre que si est la somme presque-orthogonale des espaces de Hardy, la courbe satisfait à une condition de type corde-arc, c’est-à-dire que pour tout et tout de , . Ce résultat est une sorte de réciproque à la généralisation du théorème de Calderón...
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