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Quantitative nonlinear embeddings into Lebesgue sequence spaces

    In this paper fundamental nonlinear geometries of Lebesgue sequence spaces are studied in their quantitative aspects. Applications of this work are a positive solution to the strong embeddability problem from q into p (0<p<q1) and new insights on the coarse embeddability problem from Lq into q, q>2. Relevant to geometric group theory purposes, the exact p-compression of 2 is computed. Finally coarse deformation of metric spaces with property A and locally compact amenable groups is investigated.

    AMSC: 46B20, 46B85, 46T99, 20F65


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