Abstract
In this paper, we study the boundedness results for a large class of pseudo-differential operators with smooth symbols on weighted Morrey and Weighted fractional Sobolev–Morrey spaces, respectively.
Similar content being viewed by others
References
Adams, D.R.: A note on Riesz potentials. Duke Math. J. 42, 765–778 (1975)
Calderón, A.P.: Lebesgue Spaces of Differentiable Functions and Distributions, Proc. Sympos. Pure Math., vol. 4. Amer. Math. Soc., Providence (1961)
Chiarenza, F., Frasca, M.: Morrey spaces and Hardy-Littlewood maximal function. Rend. Mat. Appl. 7, 273–279 (1987)
Coifman, R.R., Fefferman, C.: Weighted norm inequalities for maximal functions and singular integrals. Studia Math. 51, 241–250 (1974)
Hunt, R.A., Muckenhoupt, B., Wheeden, R.L.: Weighted norm inequalities for the conjugate function and Hilbert transform. Trans. Am. Math. Soc. 176, 227–251 (1973)
Komori, Y., Shirai, S.: Weighted Morrey spaces and a singular integral operator. Math. Nachr. 282(2), 219–231 (2009)
Morrey, C.B.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Am. Math. Soc. 43, 126–166 (1938)
Muckenhoupt, B.: Weighted norm inequalities for the Hardy maximal function. Trans. Am. Soc. 165, 207–226 (1972)
Muckenhoupt, B., Wheeden, R.L.: Weighted norm inequalities for fractional integrals. Trans. Am. Soc. 192, 261–274 (1974)
Rudin, W.: Real and Complex Analysis. McGraw-Hill, New York (1966)
Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gurbuz, F. Weighted Morrey and weighted fractional Sobolev–Morrey spaces estimates for a large class of pseudo-differential operators with smooth symbols. J. Pseudo-Differ. Oper. Appl. 7, 595–607 (2016). https://doi.org/10.1007/s11868-016-0158-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11868-016-0158-8
Keywords
- Weighted Morrey Space
- Weighted fractional Sobolev–Morrey Space
- Maximal operator
- Pseudo-differential Operator
- \(A_{p}\) weights