On Some Properties of the Space Lpw(Rn) and Lqt(Rn)
Abstract
In this paper, we define A
p,q(.)
w,ϑ
(R
n
) to be space of the intersection of the spaces L
p
w (R
n
) and
L
q(.)
ϑ
(R
n
). Also, we investigate some inclusions and embedding properties of the space. Moreover, we
discuss other basic properties of A
p,q(.)
w,ϑ
(R
n
).
Keywords
References
- [1] R. A. Adams, J. J. F. Fournier, Sobolev Spaces (2 nd Ed.). Academic Press, Amsterdam, (2003).
- [2] I. Aydın, On Variable Exponent Amalgam Spaces, Analele Stiintifice Ale Universitatii Ovidius onstanta-SeriaMatematica, 20(3), (2012), 5-20.
- [3] I. Aydın, Weighted Variable Sobolev Spaces and Capacity, Journal of Function Spaces and Applications, 2012,Article ID 132690, doi:10.1155/2012/132690, (2012).
- [4] I. Aydın, A. T. G¨urkanlı, On Some Properties of the Spaces Ap(x)w (Rn), Proceedings of Jangjeon Mathematical Society, 12(2), (2009), 141-155.
- [5] D. Cruz-Uribe, A. Fiorenza, C. J. Neugebauer, The Maximal Function on Variable Lp spaces, Annales Academiae Scientiarum Fennicae-Mathematica, 28, (2003), 223-238.
- [6] L. Diening, Maximal Function on Generalized Lebesgue Spaces Lp(.), Mathematical Inequalities and Applications, 7(2), (2004), 245-253.
- [7] L. Diening, P. Hast¨o, A. Nekvinda, Open Problems in Variable Exponent Lebesgue and Sobolev Spaces, In Proceedingsof the Function Spaces, Differential Operators and Nonlinear Analysis (FSDONA’ 04), Milovy, Czech, (2004), 38-58.
- [8] L. Diening, P. Harjulehto, P. Hast¨o, M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, SpringerVerlag, Berlin, (2011).
Details
Primary Language
English
Subjects
Engineering
Journal Section
Research Article
Publication Date
November 1, 2016
Submission Date
October 15, 2017
Acceptance Date
-
Published in Issue
Year 2016 Volume: 13 Number: 2