ABSTRACT
In this section we introduce and study so-called ideal spaces with mixed norm (of functions of two variables). These spaces give the natural setting for investigating partial integral operators. The most important examples are, as usual, Lebesgue spaces with mixed norm which we used (at least implicitly) already in Subsection 3.3, and Orlicz spaces with mixed norm which we will discuss in Subsection 12.3 below. The results of Subsections 12.1 and 12.2 have been obtained in KALITVIN-ZABREJKO [1991], the main results of Subsection 12.3 may be found in ApPELL-KALITVIN-ZABREJKO [1998], and the results of Subsections 12.4 and 12.5 are taken from FROLOVA-KALITVINZABREJKO [1998]. We also mention the papers KALITVIN-MILOVIDOV [1981) and POVOLOTSKIJ-KALITVIN [1986) on interpolation of partial integral operators in spaces with mixed norm.
