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SHARPMAXIMALFUNCTIONINEQUALITIESANDBOUNDEDNESSOFTOEPLITZTYPEOPERATORRELATEDTOGENERALFRACTIONALINTEGRALOPERATORS B J M A BanachJ.Math.Anal.7(2013),no.1,142–159

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Banach J. Math. Anal. 7 (2013), no. 1, 142–159

B

anach

J

ournal of

M

athematical

A

nalysis ISSN: 1735-8787 (electronic)

www.emis.de/journals/BJMA/

SHARP MAXIMAL FUNCTION INEQUALITIES AND BOUNDEDNESS OF TOEPLITZ TYPE OPERATOR RELATED TO GENERAL FRACTIONAL INTEGRAL

OPERATORS

LANZHE LIU

Communicated by L. P. Castro

Abstract. In this paper, we establish sharp maximal function inequalities for the Toeplitz type operator related to some general fractional integral operators.

As an application, we obtain the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces. The operators include Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

College of Mathematics and Econometrics, Hunan University, Changsha 410082, P. R. of China.

E-mail address: [email protected]

Date: Received: 3 June 2012; Accepted: 30 August 2012.

2010Mathematics Subject Classification. Primary 47A10; Secondary 42B20, 42B25.

Key words and phrases. Toeplitz type operator, sharp maximal function, Morrey space, BM O, Lipschitz function.

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