A Pair of Indices for Function Spaces on the Circle
نویسنده
چکیده
We give here some of the basic properties of the classes ¡4>^|, {♦ !, 1 < r < 1, of dilation operators acting in rearrangement-invariant spaces I on the circle It is shown that to each space 3E there correspond two numbers i, V, called indices, which satisfy 0 < r¡ < g < 1; these numbers represent the rate of growth or decay of ||* || as r — + 1. By using the operators + to obtain estimates for certain averaging operators A , we are able to show that the indices (rf, 77) coincide with the Boyd indices (a., /3). As a consequence, we obtain a Marcinkiewicz-type interpolation theorem for rearrangement-invariant spaces on the circle.
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