Displaying similar documents to “Singular integral characterization of nonisotropic generalized BMO spaces”

BMO-scale of distribution on ℝ n

René Erlín Castillo, Julio C. Ramos Fernández (2008)

Czechoslovak Mathematical Journal

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Let S ' be the class of tempered distributions. For f ∈ S ' we denote by J - α f the Bessel potential of f of order α . We prove that if J - α f ∈ B M O , then for any λ ∈ ( 0 , 1 ) , J - α ( f ) λ ∈ B M O , where ( f ) λ = λ - n f ( φ ( λ - 1 · ) ) , φ ∈ S . Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order α > 0 belongs to the V M O space.

On the H p - L q boundedness of some fractional integral operators

Pablo Rocha, Marta Urciuolo (2012)

Czechoslovak Mathematical Journal

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Let A 1 , ⋯ , A m be n × n real matrices such that for each 1 ≤ i ≤ m , A i is invertible and A i - A j is invertible for i ≠ j . In this paper we study integral operators of the form T f ( x ) = ∫ k 1 ( x - A 1 y ) k 2 ( x - A 2 y ) ⋯ k m ( x - A m y ) f ( y ) d y , k i ( y ) = ∑ j ∈ ℤ 2 j n / q i ϕ i , j ( 2 j y ) , 1 ≤ q i < ∞ , 1 / q 1 + 1 / q 2 + ⋯ + 1 / q m = 1 - r , 0 ≤ r < 1 , and ϕ i , j satisfying suitable regularity conditions. We obtain the boundedness of T : H p ( ℝ n ) → L q ( ℝ n ) for 0 < p < 1 / r and 1 / q = 1 / p - r . We also show that we can not expect the H p - H q boundedness of this kind of operators.

Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

Vagif Sabir Guliyev, Turhan Karaman, Rza Chingiz Mustafayev, Ayhan Şerbetçi (2014)

Czechoslovak Mathematical Journal

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In this paper, the boundedness of a large class of sublinear commutator operators T b generated by a Calderón-Zygmund type operator on a generalized weighted Morrey spaces M p , ϕ ( w ) with the weight function w belonging to Muckenhoupt’s class A p is studied. When 1 < p < ∞ and b ∈ BMO , sufficient conditions on the pair ( ϕ 1 , ϕ 2 ) which ensure the boundedness of the operator T b from M p , ϕ 1 ( w ) to M p , ϕ 2 ( w ) are found. In all cases the conditions for the boundedness of T b are given in terms of Zygmund-type integral inequalities on ( ϕ 1 , ϕ 2 ) , which...