A NOTE ON WEIGHTED COMPOSITION OPERATORS ON MEASURABLE FUNCTION SPACES

Title & Authors
A NOTE ON WEIGHTED COMPOSITION OPERATORS ON MEASURABLE FUNCTION SPACES

Abstract
In this paper we will consider the weighted composition operators W = $\small{uC_{\tau}}$ between $\small{L^{p}}$$\small{(X,\sum,\mu}$) spaces and Orlicz spaces $\small{L^{\phi}}$$\small{(X,\sum,\mu}$) generated by measurable and non-singular transformations $\small{\tau}$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\small{\tau}$ that induce weighted composition operators between $\small{L^{p}}$ -spaces by using some properties of conditional expectation operator, pair (u,$\small{{\gamma}}$) and the measure space $\small{(X,\sum,\mu}$). Also, some other properties of these types of operators will be investigated.
Keywords
weighted composition operator;conditional expectation;Fredholm operator;Orlicz space;
Language
English
Cited by
1.
Composition Operators on Cesàro Function Spaces, Journal of Function Spaces, 2014, 2014, 1
References
1.
Canad. Math. Bull., 1985. vol.28. pp.237-242

2.
J. Math. Analysis Applic., 1994. vol.187. pp.1047-1058

3.
A Hilbert space problem book, 1967.

4.
Studia Math. (Poland), 1982. vol.LXXII. pp.225-235

5.
Integral Equations Operator Theory, 2001. vol.41. pp.324-330

6.
Function spaces, 1977.

7.
Integral Equations Operator Theory, 1997. vol.29. pp.17-22

8.
Proc. Roy. Soc. Edinburgh Sect., 1991. vol.A118. pp.111-118

9.
Theory of Orlicz spaces, 1991.

10.
Proc. Amer. Math. Soc., 1976. vol.59. pp.329-333

11.
Contemp. Math., 1999. vol.232. pp.321-338

12.
Integration(2nd ed.), 1967.