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Open Access Research

Boundedness of fractional oscillatory integral operators and their commutators on generalized Morrey spaces

Ahmet Eroglu

Author Affiliations

Department of Mathematics, Nigde University, Nigde, Turkey

Boundary Value Problems 2013, 2013:70  doi:10.1186/1687-2770-2013-70

Published: 2 April 2013

Abstract

In this paper, it is proved that both oscillatory integral operators and fractional oscillatory integral operators are bounded on generalized Morrey spaces <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/70/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/70/mathml/M1">View MathML</a>. The corresponding commutators generated by BMO functions are also considered.

MSC: 42B20, 42B25, 42B35.

Keywords:
generalized Morrey space; oscillatory integral; commutator; BMO spaces