Displaying similar documents to “Notes on interpolation inequalities.”

Pointwise multipliers on weighted BMO spaces

Eiichi Nakai (1997)

Studia Mathematica

Similarity:

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 × + + , 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...

The commutators of analysis and interpolation

Cerdà, Joan

Similarity:

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...

Weighted inequalities for commutators of one-sided singular integrals

María Lorente, María Silvina Riveros (2002)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We prove weighted inequalities for commutators of one-sided singular integrals (given by a Calder’on-Zygmund kernel with support in ( - , 0 ) ) with BMO functions. We give the one-sided version of the results in C. Pérez, Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function, J. Fourier Anal. Appl., vol. 3 (6), 1997, pages 743–756 and C. Pérez, Endpoint estimates for commutators of singular integral operators, J. Funct. Anal., vol 128 (1),...