Loading...
5 results
Search Results
Now showing 1 - 5 of 5
- Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spacesPublication . Guliyev, Vagif S.; Hasanov, Javanshir J.; Samko, StefanWe consider local "complementary" generalized Morrey spaces M-c({x0})p(.).omega (Omega) in which the p-means of function are controlled over Omega \ B(x(0), r) instead of B(x(0), r), where Omega subset of R-n is a bounded open set, p(x) is a variable exponent, and no monotonicity type condition is imposed onto the function omega(r) defining the "complementary" Morrey-type norm. In the case where omega is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev type M-c({x0})p(.).omega (Omega) -> M-c({x0})p(.).omega (Omega)-theorem for the potential operators I-alpha(.), also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities-on omega(r), which do not assume any assumption on monotonicity of omega(r).
- Maximal operator in variable exponent generalized morrey spaces on quasi-metric measure spacePublication . Guliyev, Vagif S.; Samko, StefanWe consider generalized Morrey spaces on quasi-metric measure spaces , in general unbounded, with variable exponent p(x) and a general function defining the Morrey-type norm. No linear structure of the underlying space X is assumed. The admission of unbounded X generates problems known in variable exponent analysis. We prove the boundedness results for maximal operator known earlier only for the case of bounded sets X. The conditions for the boundedness are given in terms of the so called supremal inequalities imposed on the function , which are weaker than Zygmund-type integral inequalities often used for characterization of admissible functions . Our conditions do not suppose any assumption on monotonicity of in r.
- Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-morrey spacesPublication . Deringoz, Fatih; Guliyev, Vagif S.; Samko, StefanWe prove the boundedness of the Hardy-Littlewood maximal operator and their commutators with BMO-coefficients in vanishing generalized Orlicz-Morrey spaces VM Phi,phi(R-n) including weak versions of these spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators involving the Young function Phi(u) and the function phi(x, r) defining the space. No kind of monotonicity condition on phi(x, r) in r is imposed.
- Vanishing generalized Orlicz-Morrey spaces and fractional maximal operatorPublication . Deringoz, Fatih; Guliyev, Vagif S.; Samko, StefanWe find sufficient conditions for the non-triviality of the generalized Orlicz-Morrey spaces M-Phi,M-phi (R-n), and prove the boundedness of the fractional maximal operator and its commutators with BMO-coefficients in vanishing generalized Orlicz-Morrey spaces VM Phi,phi (R-n) including weak versions of these spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators involving the Young functions Phi(u), Psi(u) and the function phi(x,r) defining the space. No kind of monotonicity condition on phi(x,r) in r is imposed.
- Commutators of fractional maximal operator in variable Lebesgue spaces over bounded quasi‐metric measure spacesPublication . Guliyev, Vagif S.; Samko, StefanWe study the fractional maximal commutators Mb,𝜂 and the commutators[b, M𝜂] of the fractional maximal operator with b ∈ BMO(X) in the variable Lebesgue spaces Lp(·)(X) over bounded quasi-metric measure spaces. We give necessary and sufficient conditions for the boundedness of the operators Mb,𝜂 and [b, M𝜂] on the spaces Lp(·)(X) when b ∈ BMO(X). Furthermore, we obtain some new characterizations for certain subspaces of BMO(X).