Displaying similar documents to “An atomic decomposition of the predual of BMO(ρ).”

Hardy spaces and the Dirichlet problem on Lipschitz domains.

Carlos E. Kenig, Jill Pipher (1987)

Revista Matemática Iberoamericana

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Our concern in this paper is to describe a class of Hardy spaces H(D) for 1 ≤ p < 2 on a Lipschitz domain D ⊂ R when n ≥ 3, and a certain smooth counterpart of H(D) on R, by providing an atomic decomposition and a description of their duals.

Pointwise multipliers on weighted BMO spaces

Eiichi Nakai (1997)

Studia Mathematica

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Let E and F be spaces of real- or complex-valued functions defined on a set X. A real- or complex-valued function g defined on X is called a pointwise multiplier from E to F if the pointwise product fg belongs to F for each f ∈ E. We denote by PWM(E,F) the set of all pointwise multipliers from E to F. Let X be a space of homogeneous type in the sense of Coifman-Weiss. For 1 ≤ p < ∞ and for ϕ : X × ℝ + → ℝ + , we denote by b m o ϕ , p ( X ) the set of all functions f ∈ L l o c p ( X ) such that s u p a ∈ X , r > 0 1 / ϕ ( a , r ) ( 1 / μ ( B ( a , r ) ) ʃ B ( a , r ) | f ( x ) - f B ( a , r ) | p d μ ) 1 / p < ∞ , where B(a,r) is the ball centered...

Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients

Péter Simon, Ferenc Weisz (1997)

Studia Mathematica

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Our main result is a Hardy type inequality with respect to the two-parameter Vilenkin system (*) ( ∑ k = 1 ∞ ∑ j = 1 ∞ | f ̂ ( k , j ) | p ( k j ) p - 2 ) 1 / p ≤ C p ∥ f ∥ H * * p (1/2 < p≤2) where f belongs to the Hardy space H * * p ( G m × G s ) defined by means of a maximal function. This inequality is extended to p > 2 if the Vilenkin-Fourier coefficients of f form a monotone sequence. We show that the converse of (*) also holds for all p > 0 under the monotonicity assumption.