In this paper, some sharp inequalities for certain multilinear operators related to the Littlewood-Paley operator and the Marcinkiewicz operator are obtained. As an application, we obtain the (L p , L q)-norm inequalities and Morrey spaces boundedness for the multilinear operators.

Malposition of the acetabular component is a leading cause of dislocation in total hip arthroplasty (Woo, 1982). The two most influential surgeon-controlled variables are thought to be abduction (tilt) and anteversion of the cup. Empirically, while 30-50° of tilt and 5-25° of anteversion is felt to be a “safe-zone” (Morrey, 1992), dislocation nevertheless remains a disturbingly frequent occurre...

Let Ω be an open bounded set in R n (n ≥ 2), with C 2 boundary, and N p,λ (Ω) (1 < p < +∞, 0 ≤ λ < n) be a weighted Morrey space. In this note we prove a weighted version of the Miranda-Talenti inequality and we exploit it to show that, under a suitable condition of Cordes type, the Dirichlet problem:

We prove an apriori estimate in Morrey spaces for both intrinsic and extrinsic biharmonic maps into spheres. As applications, we prove an energy quantization theorem for biharmonic maps from 4-manifolds into spheres and a partial regularity for stationary intrinsic biharmonic maps into spheres. x

In this paper under some growth condition we investigate the connection between RBMO and the Morrey spaces. We do not assume the doubling condition which has been a key property of harmonic analysis. We also obtain another type of equivalent norms.

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Blow-up criteria of smooth solutions for the 3D micropolar fluid equations are investigated. Logarithmically improved blow-up criteria are established in the Morrey-Campanto space.

We give a natural definition of the Morrey spaces for Radon measures which may be non-doubling but satisfy the growth condition. In these spaces we investigate the behavior of the maximal operator, the fractional integral operator, the singular integral operator and their vector-valued extensions.

BACKGROUND The olecranon approach has been the gold standard for surgical approaches to fracture fixation of distal articular surface of humerus. Although it provides a good exposure, it also has disadvantages of delayed union, nonunion and implant related complications at the osteotomy site. OBJECTIVE The aim of this study was to determine the functional outcome of displaced intra-articular ...

We establish the global well-posedness of the Landau-Lifshitz-Gilbert equation in Rn for any initial data m0 ∈ H1 ∗(R, S2) whose gradient belongs to the Morrey space M2,2(Rn) with small norm ‖∇m0‖M2,2(Rn). The method is based on priori estimates of a dissipative Schrödinger equation of GinzburgLandau types obtained from the Landau-Lifshitz-Gilbert equation by the moving frame technique.

Let L = −∆ + V (x) be a Schrödinger operator, where ∆ is the Laplacian on R, while nonnegative potential V (x) belonging to the reverse Hölder class. We establish the boundedness of the commutators of Marcinkiewicz integrals with rough kernel associated with schrödinger operator on vanishing generalized Morrey spaces.