We introduce and study the family of Besov–Köthe spaces which is a generalization of the Besov spaces, the Besov–Morrey spaces and the variable Besov spaces. As an application of the general results for the Besov–Köthe spaces, we identify a pre-dual of the Besov–Morrey space.

In this paper, the authors introduce the anisotropic Herz-Morrey spaces with two variable exponents and obtain some properties of these spaces. Subsequently as an application, the authors give some boundedness on the anisotropic Herz-Morrey spaces with two variable exponents for a class of sublinear operators, which extend some known results.

We consider generalized Morrey spaces Mp,ω R with a general function ω x, r defining the Morrey-type norm. We find the conditions on the pair ω1, ω2 which ensures the boundedness of the maximal operator and Calderón-Zygmund singular integral operators from one generalized Morrey space Mp,ω1 R to another Mp,ω2 R , 1 < p < ∞, and from the space M1,ω1 R to the weak space WM1,ω2 R . We also prove a...

R A O’Donnell, C Peebles, J A Ward, A Daraker, G Angco, P Broberg, S Pierrou, J Lund, S T Holgate, D E Davies, D J Delany, S J Wilson, R Djukanovic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

We investigate geometric curvature energies on closed curves involving integral versions of the Menger curvature. In particular, we prove geometric variants of Morrey-Sobolev and Morrey-space imbedding theorems, which may be viewed as counterparts to respective results on one-dimensional sets in the context of harmonic analysis. Mathematics Subject Classification (2010): 28A75 (primary); 53A04,...

In this paper, we consider the problem of boundedness of Hausdorff operator on weighted central Morrey spaces. In particular, we obtain sharp bounds for Hausdorff operators on power weighted central Morrey spaces. Analogous results for the commutators of Hausdorff operators when the symbol functions belong to weighted central-BMO spaces are obtained as well.

We establish a decomposition of Besov-Morrey spaces in terms of smooth “wavelets” obtained from a Littlewood-Paley partition of unity, or more generally molecules concentrated on dyadic cubes. We show that an expansion in atoms supported on dyadic cubes holds. We study atoms in Morrey spaces and prove a Littlewood-Paley theorem. Our results extend those of M. Frazier and B. Jawerth for Besov sp...

In this paper, we give the necessary and sufficient conditions for boundedness of Hardy-Ces?ro operators on some weighted function spaces such as central Morrey, local non-local Herz Morrey-Herz type with variable exponent.

The aim of the study was to explore the clinical outcome of posterolateral and anteromedial approaches in treatment of terrible triad of the elbow. The study involved 12 patients with closed terrible triad of the elbow treated by posterolateral and anteromedial approaches between January 2010 and June 2012. The mechanism of injury included fall from height in 9 patients and traffic accident in ...

PURPOSE Radiographic arthrosis is a common sequela of elbow trauma. Few studies have addressed risk factors for radiographic arthrosis after elbow injury, especially in the long term. Data from multiple long-term follow-up studies of patients with surgically treated elbow fractures provided us with an opportunity to assess risk factors for long-term radiographic arthrosis after elbow injury. ...