1. Introduction. The Calderón-Zygmund theory of singular integrals has been traditionally considered with respect to a measure satisfying a doubling condition. Recently, Tolsa [T] and, independently, Nazarov, Treil, and Volberg [NTV] have shown that this standard doubling condition was not really necessary. Likewise, in the homogeneous spaces setting, functions of bounded mean oscillation, BMO,...

Let L = −∆+ V be a Schrödinger operator on R, d ≥ 3, where V is a nonnegative function, V 6= 0, and belongs to the reverse Hölder class RHd/2. The purpose of this paper is three-fold. First, we prove a version of the classical theorem of Jones and Journé on weak∗-convergence in H L(R ). Secondly, we give a bilinear decomposition for the product space H L(R )×BMOL(R). Finally, we study the commu...

H ·H := ̆ h = fg : f, g ∈ H ̄ = H ←↩ H is the product space of H2, by inner/outer factorization and Cauchy-Schwarz inequality. It is interesting, then, to find the dual space of H1. C. Fefferman [7] proved that, under the H2 paring (with some care), (H2 ·H2)∗ = (H1)∗ = BMO∩H(D) is the space of the analytic functions with bounded mean oscillation. The definition of BMO, born out of a problem in el...

With the use of real-variable techniques, we construct a weight function ω on interval [0,2π) which is doubling and satisfies logω BMO function, but not Muckenhoupt (A∞). Applications to BMO–Teichmüller space chord-arc curves are considered.

In this paper we show that the theory of Hankel operators in the torus T , for d > 1, presents striking differences with that on the circle T, starting with bounded Hankel operators with no bounded symbols. Such differences are circumvented here by replacing the space of symbols L∞(T) by BMOr(T), a subspace of product BMO, and the singular numbers of Hankel operators by so-called sigma numbers....

PURPOSE To delineate three dimensionally the neural canal landmarks-Bruch's membrane opening (BMO), anterior sclera canal opening (ASCO), anterior laminar insertion (ALI), posterior laminar insertion (PLI), and posterior scleral canal opening (PSCO)-and the anterior-most aspect of the subarachnoid space (ASAS), within digital three-dimensional (3-D) reconstructions of the monkey optic nerve hea...

The aim of this paper is a) if Σak2 < ∞ then Σak rk(x) is in BMO that{rk(x)} is Rademacher system. b) P1k=1 ak!nk (x) 2 BMO; 2k nk < 2k+1that f!n(x)g is Walsh system. c) If jakj < 1k then P1k=1 ak!k(x) 2 BMO.