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Old and new Morrey spaces with heat kernel bounds. (English) Zbl 1133.42017

The authors discuss the concept of Morrey space and introduce a new version of it. They replace the value of a parameter appearing in its definition with a quantity related to the infinitesimal generator of a suitable analytic semigroup. Using this idea, they get a characterization of the “new” Morrey space. They also discuss the equivalence of the new and the classical Morrey space.

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B35 Function spaces arising in harmonic analysis

Keywords:

semigroups
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