Abstract

We prove new interpolation theorems for a sufficiently wide class of nonlinear operators in Morrey-type spaces. In particular, these theorems apply to Urysohn integral operators. We also obtain analogs of the Marcinkiewicz–Calderón and Stein–Weiss–Peetre interpolation theorems and establish a criterion of \((p,q)\) quasiweak boundedness of the Urysohn operator.

中文翻译：

---

广义Morrey型空间中非线性算子的插值定理及其应用。

摘要

我们证明了在Morrey型空间中足够广泛的一类非线性算子的新插值定理。这些定理尤其适用于Urysohn积分算子。我们还获得了Marcinkiewicz-Calderón和Stein-Weiss-Peetre插值定理的类似物，并建立了Urysohn算子的\（（p，q）\）拟弱有界性的准则。