Some remarks on the $L^P$-$L^q$ boundedness of $uC_{varphi}$

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

In this paper we will consider the weighted composition operators between two different $L^P$- spaces and then we characterize the functions u and transformations $varphi$ that induce weighted composition operator $uC_{varphi}$ between $L^p(X,Sigma, mu)$-spaces by using some properties of conditional expectation operator, pair (u, $varphi$) and the measure space $(X,Sigma,mu)$.

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[1] Campbell, J., Jamison, J.: On some classes of weighted composition operators, Glasgow Math. J. 32, 87-94, (1990).
[2] Dunford, N., Schwartz, J. T.: Linear Operators, Part I, Interscience, New York, 1971.
[3] Hoover, T., Lambert, T., Quinn, J.: The Markov process determined by a weighted composition operator. Studia Math. (Poland) LXXII, 225-235, (1982).
[4] Jabbarzadeh, M. R., Pourreza, E.: A note on weighted composition operators on $L^p$-spaces, Bull. Iranian Math. Soc. 29, 47-54, (2002).
[5] Rao, M. M.: Conditional measure and applications, Marcel Dekker, New York, 1993.
[6] Singh, R. K.: Composition operators induced by rational functions, Proc. Amer. Math. Soc. 59, 329-333, (1976).
[7] Takagi, H., Yokouchi, K.: Multiplication and composition operators between two $L^p$- spaces , Contemp. Math. 232, 321-338, (1999).