BILINEAR FRACTIONAL INTEGRAL OPERATORS ON GRAND MORREY SPACES AND GRAND HARDY-MORREY SPACES

초록

We establish the boundedness of bilinear fractional integral operators on grand Morrey spaces and grand Hardy-Morrey spaces. Our approach combines a refined extrapolation method with sparse domination techniques, extending recent results on linear fractional integrals to the multilinear setting. The key innovation is the adaptation of the extrapolation machinery to handle the nonlinear nature of bilinear operators while preserving the delicate balance between the fractional parameter and the integrability indices. As applications, we obtain bilinear Sobolev embeddings and fractional Leibniz rules in the grand Morrey space framework.

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