We consider the Dirichlet problem { Lu = 0 in D u = g on ∂D for two second order elliptic operators Lku = ∑n i,j=1 a i,j k (x) ∂iju(x), k = 0, 1, in a bounded Lipschitz domain D ⊂ IR. The coefficients a k belong to the space of bounded mean oscillation BMO with a suitable small BMO modulus. We assume that L0 is regular in L(∂D, dσ) for some p, 1 < p < ∞, that is, ‖Nu‖Lp ≤ C ‖g‖Lp for all contin...

Let μ be a Radon measure on R, which may be non doubling. The only condition that μ must satisfy is the size condition μ(B(x, r)) ≤ C r, for some fixed 0 < n ≤ d. Recently, the author introduced spaces of type BMO(μ) and H(μ) with properties similar to ones of the classical spaces BMO and H defined for doubling measures. These new spaces proved to be useful to study the L(μ) boundedness of Cald...

We introduce a new class of Hardy spaces H(R), called Hardy spaces of Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garćıa-Cuerva, Strömberg, and Torchinsky. Here, φ : R × [0,∞) → [0,∞) is a function such that φ(x, ·) is an Orlicz function and φ(·, t) is a MuckenhouptA∞ weight. A function f belongs to H(R) if and only if its maximal fu...

Functions of bounded mean oscillation (BMO) play an important role in complex function theory and harmonic analysis. In this paper a sampling theorem for bandlimited BMO-functions is derived for sampling points that are the zero sequence of some sine-type function. The class of sinetype functions is large and, in particular, contains the sine function, which corresponds to the special case of e...

In this paper, the authors obtain continuity of a class linear operators on variable anisotropic Hardy--Lorentz spaces. addition, also that dual space Hardy-Lorentz spaces is BMO-type with exponents. This result still new even when exponent function $p(\cdot)$ $p$.

PURPOSE This study explores variation in the axial location of Bruch's membrane opening (BMO) to determine if this reference plane varies with age and race. METHODS There were 168 spectral-domain optical coherence tomography (SDOCT) optic nerve head volumes that were obtained from healthy subjects and manually delineated within 24 axial slices to develop point clouds for Bruch's membrane and ...

PURPOSE This study examined the association between peripapillary choroidal thickness (PCT) with age and race in a group of African descent (AD) and European descent (ED) subjects with normal eyes. METHODS Optic nerve head images from enhanced depth imaging spectral-domain optical coherence tomography of 166 normal eyes from 84 subjects of AD and ED were manually delineated to identify the pr...

We address $L^p(\mu)\to L^p(\lambda)$ bounds for paraproducts in the Bloom setting. introduce certain “sparse BMO” functions associated with sparse collections no infinitely increasing chains, and use these to express operators as sums of martingale transforms – essentially, Haar multipliers well obtain an equivalence norms between $\mathcal{A}\_{\mathcal{S}}$ compositions $\Pi^\*\_a\Pi\_b$.

In this paper we show how to compute the Λα norm , α ≥ 0, using the dyadic grid. This result is a consequence of the description of the Hardy spaces H(R ) in terms of dyadic and special atoms. Recently, several novel methods for computing the BMO norm of a function f in two dimensions were discussed in [9]. Given its importance, it is also of interest to explore the possibility of computing the...

We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of C. In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not suitable. Several properties (the Garsia-norm equivalent theorem, Carleson measure, and so on) of BMOA spaces are extended to the operator-valued setting. Then, the operat...