The seminal paper of Coifman et al. (1993) has triggered numerous new applications of Hardy spaces and the space BMO of functions of bounded mean oscillation to nonlinear partial differential equations. These applications include various problems of variational and geometric origin: harmonic and p-harmonic maps, H-systems, wave maps; (see, e.g., Bethuel, 1993; Evans, 1991; Hélein, 1998, 2002; T...

Let f be a Borel measurable function of the complex plane to itself. We consider the nonlinear operator Tf defined by Tf [g] = f ◦ g, when g belongs to a certain subspace X of the space BMO(Rn) of functions with bounded mean oscillation on the Euclidean space. In particular, we investigate the case in which X is the whole of BMO, the case in which X is the space VMO of functions with vanishing ...

The functions with bounded mean oscillation (BMO) have been shown to be immense interest in several areas of analysis and probability. We introduce BMO-type space BMOHK(Rn) for non-absolute integrable functions. Various properties completion are included. Relations between the classical BMO investigated.

We study the condition that characterizes the symbols of bounded Hankel operators on the Bergman space of a strongly pseudoconvex domain and show that it is equivalent to BMO plus analytic. (Here we mean the Bergman metric BMO of Berger, Coburn and Zhu.) In the course of the proof we obtain new d -estimates that may be of independent interest. Some applications include a decomposition of BMO si...

In this paper, we prove the well-posedness for the fractional NavierStokes equations in critical spaces G −(2β−1) n (R ) and BMO−(2β−1)(Rn). Both of them are close to the largest critical space Ḃ −(2β−1) ∞,∞ (R ). In G −(2β−1) n (R ), we establish the well-posedness based on a priori estimates for the fractional Navier-Stokes equations in Besov spaces. To obtain the well-posedness in BMO−(2β−1)...

The duality between Hl and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained . Using the atomic decomposition approach ([C], [L]) the author studied the problem of characterizing the dual space of Hl of vector-valued functions . In [B2] the author showed, for the case SZ = {Iz1 = 1}, tha...

We prove that the Bloch space coincides with the space BMOA in the tube over the spherical cone of R.3; this extends a well-known onedimensional result. Introduction. Let Q be a symmetric Siegel domain of type II contained in Cn. Let V denote the Lebesgue measure in fi and H{Q) the space of holomorphic (or analytic) functions in fi. When n = 1 and fi = tt+ = {z £ C: Imz > 0}, a Bloch function i...

We determine the distance (up to a multiplicative constant) in Zygmund class $\Lambda_{\ast}(\mathbb{R}^n)$ subspace $\mathrm{J}(\mathbf{bmo})(\mathbb{R}^n).$ The latter space is image under Bessel potential $J := (1-\Delta)^{-1/2}$ of $\mathbf{bmo}(\mathbb{R}^n),$ which non-homogeneous version classical $\mathrm{BMO}.$ Locally, $\mathrm{J}(\mathbf{bmo})(\mathbb{R}^n)$ consists functions that t...

Abstract In this manuscript two BMO estimates are obtained, one for Linear Elasticity and Nonlinear Elasticity. It is first shown that the BMO-seminorm of gradient a vector-valued mapping bounded above by constant times symmetric part its gradient, is, Korn inequality in BMO. The uniqueness equilibrium finite deformation whose principal stresses everywhere nonnegative then considered. when seco...