Displaying similar documents to “A geometrical/combinatorical question with implications for the John-Nirenberg inequality for BMO functions”

Monotonic rearrangements of functions with small mean oscillation

Dmitriy M. Stolyarov, Vasily I. Vasyunin, Pavel B. Zatitskiy (2015)

Studia Mathematica

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We obtain sharp bounds for the monotonic rearrangement operator from "dyadic-type" classes to "continuous" ones; in particular, for the BMO space and Muckenhoupt classes. The idea is to connect the problem with a simple geometric construction named α-extension.

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...

An embedding relation for bounded mean oscillation on rectangles

Benoît F. Sehba (2014)

Annales Polonici Mathematici

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In the two-parameter setting, we say a function belongs to the mean little BMO if its mean over any interval and with respect to any of the two variables has uniformly bounded mean oscillation. This space has been recently introduced by S. Pott and the present author in relation to the multiplier algebra of the product BMO of Chang-Fefferman. We prove that the Cotlar-Sadosky space b m o ( N ) of functions of bounded mean oscillation is a strict subspace of the mean little BMO.

Oblique derivative problems for the laplacian in Lipschitz domains.

Jill Pipher (1987)

Revista Matemática Iberoamericana

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The aim of this paper is to extend the results of Calderón [1] and Kenig-Pipher [12] on solutions to the oblique derivative problem to the case where the data is assumed to be BMO or Hölder continuous.

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 &lt; p &lt; ∞ , if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.