Notes on interpolation inequalities.

Dong, Jiu-Gang; Xiao, Ti-Jun

Displaying similar documents to “Notes on interpolation inequalities.”

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 $ϕ : X \times ℝ_{+} \to ℝ_{+}$ , we denote by $b m o_{ϕ, p} (X)$ the set of all functions $f \in L_{l o c}^{p} (X)$ such that $s u p_{a \in X, r > 0} 1 / ϕ (a, r) (1 / μ (B (a, r)) ʃ_{B (a, r)} | f (x) - f_{B (a, r)} {|^{p} d μ)}^{1 / p} < \infty$ , where B(a,r) is the ball centered...

The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent

Jingshi Xu (2007)

Czechoslovak Mathematical Journal

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The boundednees of multilinear commutators of Calderón-Zygmund singular integrals on Lebesgue spaces with variable exponent is obtained. The multilinear commutators of generalized Hardy-Littlewood maximal operator are also considered.

Sharp weights and BMO-preserving homeomorphisms

Steven Bloom (1990)

Studia Mathematica

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The commutators of analysis and interpolation

Cerdà, Joan

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The boundedness properties of commutators for operators are of central importance in Mathematical Analysis, and some of these commutators arise in a natural way from interpolation theory. Our aim is to present a general abstract method to prove the boundedness of the commutator $[T, Ω]$ for linear operators $T$ and certain unbounded operators $Ω$ that appear in interpolation theory, previously known and a priori unrelated for both real and complex interpolation methods, and also to show how the...