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

BMO-scale of distribution on 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 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 ( n ) L q ( 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.