WEIGHTED NORM INEQUALITIES OF GENERALIZED WEIGHTED HARDY-CESÀRO OPERATORS AND COMMUTATORS WITH SYMBOLS IN CMO SPACES ON GENERALIZED WEIGHTED MORREY SPACES
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Abstract
In this work, our main aim is to study the boundedness of the weighted Hardy-Cesàro operators and commutators on generalized weighted Morrey spaces . We establish certain sufficient conditions which imply the boundedness of the weighted Hardy-Cesàro operators and their commutators with symbols in CMO spaces on generalized weighted Morrey spaces .
Keywords
weighted Hardy-Cesàro operator, commutator, generalized weighted Morrey space, CMO space
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References
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Tang, C., & Zhou, R. (2012). Boundedness of weighted Hardy operator and its applications on Triebel-Lizorkin-type spaces. Journal of Function Spaces and Applications 2012, 1-9.
Xiao, J. (2001). and BMO bounds of weighted Hardy-Littlewood averages. J. Math. Anal. Appl., 262, 660-666.
Duoandikoetxea, J. (2000). Fourier Analysis, Grad. Stud. Math., (29), American Math. Soc., Providence.
Folland, G. B. (1999). Real Analysis: Modern Techniques and Their Applications. John Wiley and Sons, second edition.
Fu, Z. W., Liu, Z. G., & Lu, S. Z. (2009). Commutators of weighted Hardy operators on . Proc. Amer. Math. Soc., 137(10), 3319-3328.
Fu, Z. W., & Lu, S. Z. (2010). Weighted Hardy operators and commutators on Morrey spaces. Front. Math. China, 5(3), 531-539.
Guliyev, V. S. (2012). Generalized weighted Morrey spaces and higher order commutators of sublinear operators. Eurasian Math. J., 3(3), 33-61.
Hardy, G. H., Littlewood, J. E., & Polya, G. (1952). Inequalities. London/New York: Cambridge University Press, (2nd edition).
John, F., & Nirenberg, L. (1961). On functions of bounded mean oscillation. Comm. Pure and Appl. Math., 14, 415-426.
Kuang, J. (2010). Weighted Morrey-Herz spaces and applications. Applied Mathematics E-Notes 10, 159-166.
Mizuhara, T. (1991). Boundedness of some classical operators on generalized Morrey spaces. Harmonic Analysis, ICM 90 Satellite Proceedings, Springer - Verlag, Tokyo, 183-189.
Tang, C., & Zhou, R. (2012). Boundedness of weighted Hardy operator and its applications on Triebel-Lizorkin-type spaces. Journal of Function Spaces and Applications 2012, 1-9.
Xiao, J. (2001). and BMO bounds of weighted Hardy-Littlewood averages. J. Math. Anal. Appl., 262, 660-666.