BOUNDEDNESS OF INTEGRAL OPERATORS ON GENERALIZED MORREY SPACES AND ITS APPLICATION TO SCHRODINGER OPERATORS

By K. Kurata, Sei-ichi Nishigaki, Satoko Sugano. 2000

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Weighted Hardy and potential operators in the generalized Morrey spaces (2011, unknown): “On a non-weighted p → q-boundedness of potential operators in the generalized Morrey spaces Potential operators in the non-weighed setting were studied in [12,14,15,17,23,28,40].”
A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces (2012, unknown): “Later, this type of function spaces was used in [44, 56, 76].”
Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces (2010, background): “Generalized Morrey spaces of such a kind in the case of constant p were studied in [4], [13], [26], [28], [30], [31].”
A Thought on Generalized Morrey Spaces (2018, methodology): “See [62] for applicatitons to Schrödinger equations.”
ON GENERALIZED FRACTIONAL INTEGRAL OPERATORS (2004, unknown): “[6].”
Fractional Integrals and Generalized Olsen Inequalities (2009, background): “[12] extended Olsen’s result by proving that, for some p > 1 and a function φ satisfying several conditions (including the doubling condition), the operator W · Iα is bounded on generalized Morrey spaces Mp,φ, provided that W ∈Ms1,φ ∩Ms2,φ for some indices s1 and s2.”