Displaying similar documents to “Monotonic rearrangements of functions with small mean oscillation”

BMO and commutators of martingale transforms

Svante Janson (1981)

Annales de l'institut Fourier

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The commutator of multiplication by a function and a martingale transform of a certain type is a bounded operator on L p , 1 < p < ∞ , if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.

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...

A geometrical/combinatorical question with implications for the John-Nirenberg inequality for BMO functions

Michael Cwikel, Yoram Sagher, Pavel Shvartsman (2011)

Banach Center Publications

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The first and last sections of this paper are intended for a general mathematical audience. In addition to some very brief remarks of a somewhat historical nature, we pose a rather simply formulated question in the realm of (discrete) geometry. This question has arisen in connection with a recently developed approach for studying various versions of the function space BMO. We describe that approach and the results that it gives. Special cases of one of our results give alternative proofs...