Mathematics – Functional Analysis
Scientific paper
2011-09-26
Mathematics
Functional Analysis
Scientific paper
We consider local "complementary" generalized Morrey spaces ${\dual \cal M}_{\{x_0\}}^{p(\cdot),\om}(\Om)$ in which the $p$-means of function are controlled over $\Om\backslash B(x_0,r)$ instead of $B(x_0,r)$, where $\Om \subset \Rn$ is a bounded open set, $p(x)$ is a variable exponent, and no monotonicity type conditio is imposed onto the function $\om(r)$ defining the "complementary" Morrey-type norm. In the case where $\om$ 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 ${\dual \cal M}_{\{x_0\}}^{p(\cdot),\om} (\Om)\rightarrow {\dual \cal M}_{\{x_0\}}^{q(\cdot),\om} (\Om)$-theorem for the potential operators $I^{\al(\cdot)},$ also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities on $\om(r)$, which do not assume any assumption on monotonicity of $\om(r)$.
Guliyev Vagif S.
Hasanov Javanshir J.
Samko Stefan G.
No associations
LandOfFree
Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-689339