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1.
In this paper, we consider a class of Banach space valued singular integrals. The Lp boundedness of these operators has already been obtained. We shall discuss their boundedness from BMO to BMO. As applications, we get BMO boundednessfor the classic g-function and the Marcinkiewicz integral. Some known results are improved.  相似文献   

2.
Sharp inequalities between weight bounds from A 2-condition and the BMO norm or the distance from L in the BMO norm are obtained in the one dimensional case.  相似文献   

3.
The present paper is concerned with elliptic systems with BMO coefficients: div(Au)=divF, where A(x) is a positive definite matrix whose entries are in BMO and F is a given matrix field in L p . We show existence and uniqueness of the distributional solution of class W 1,p , provided p is close to 2, depending on the BMO norm of A. This result is achieved using a refinement of a classical Theorem of Coifman Rochberg and Weiss about commutators with BMO functions.  相似文献   

4.
On the Blow-up Criterion of Smooth Solutions to the MHD System in BMO Space   总被引:1,自引:0,他引:1  
In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let (u(x,t),b(x,t)) be smooth solutions in (0, T). It is shown that the solution (u(x, t), b(x, t)) can be extended beyond t = T if (u(x,t), b(x, t)) ∈ L^1 (0, T; BMO) or the vorticity (rot u(x, t), rot b(x, t)) ∈ L^1 (0, T; BMO) or the deformation (Def u(x, t), Def b(x, t)) ∈ L^1 (0, T; BMO).  相似文献   

5.
We study boundedness properties of a class ofmultiparameter paraproducts on the dual space of the dyadic Hardy space H d 1 (T N ), the dyadic product BMO space BMO d (T N ). For this, we introduce a notion of logarithmic mean oscillation on the polydisc. We also obtain a result on the boundedness of iterated commutators on BMO [0, 1] N ).  相似文献   

6.
Extending results of Staples and Smith-Stegenga, we characterize measurable subsets of a given domainDR n on which BMO(D) functions areL p integrable or exponentially integrable. In particular, we characterize uniform domains by the integrability of BMO functions. We also remark on the boundedness of domains satisfying a certain integrability condition for the quasihyperbolic metric.  相似文献   

7.
This paper establishes the local (or global, resp.) well-posedness of the heat flow of biharmonic maps from ℝ n to a compact Riemannian manifold without boundary for initial data with small local BMO (or BMO, resp.) norms.  相似文献   

8.
In this paper, we obtain Lipschitz and BMO norm inequalities for the composition G ∘ T of the homotopy operator T and Green’s operator G applied to differential forms. We also investigate the relationship among Lipschitz norm, BMO norm and L s norm.  相似文献   

9.
Consider a second order divergence form elliptic operator L with complex bounded measurable coefficients. In general, operators based on L, such as the Riesz transform or square function, may lie beyond the scope of the Calderón–Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some L p spaces. In this work we develop a theory of Hardy and BMO spaces associated to L, which includes, in particular, a molecular decomposition, maximal and square function characterizations, duality of Hardy and BMO spaces, and a John–Nirenberg inequality. S. Hofmann was supported by the National Science Foundation.  相似文献   

10.
We establish a connection between the absolute continuity of elliptic measure associated with a second order divergence form operator with bounded measurable coefficients with the solvability of an end-point BMO Dirichlet problem. We show that these two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the BMO Dirichlet problem implies L p solvability for all p>p 0.  相似文献   

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