Bilinear embedding in Orlicz spaces for divergence-form operators with complex coefficients

Kristina Ana \v{S}kreb; Vjekoslav Kova\v{c}

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Bilinear embedding in Orlicz spaces for divergence-form operators with complex coefficients

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arxiv 2110.15812 v2 pith:T64IKWWV submitted 2021-10-29 math.FA math.APmath.CA

Bilinear embedding in Orlicz spaces for divergence-form operators with complex coefficients

Vjekoslav Kova\v{c} , Kristina Ana \v{S}kreb This is my paper

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keywords embeddingfunctionsoperatorsachievebehavebellmanbi-sublinearbilinear

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We prove a bi-sublinear embedding for semigroups generated by non-smooth complex-coefficient elliptic operators in divergence form and for certain mutually dual pairs of Orlicz-space norms. This generalizes a result by Carbonaro and Dragi\v{c}evi\'{c} from power functions to more general Young functions that still behave like powers. To achieve this, we generalize a Bellman function constructed by Nazarov and Treil.

Bilinear embedding in Orlicz spaces for divergence-form operators with complex coefficients

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