Basic functional properties of certain scale of rearrangement-invariant spaces |
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Authors: | Hana Tur?inová |
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Institution: | Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic |
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Abstract: | We define a new scale of function spaces governed by a norm-like functional based on a combination of a rearrangement-invariant norm, the elementary maximal function, and powers. A particular instance of such spaces surfaced recently in connection with optimality of target function spaces in general Sobolev embeddings involving upper Ahlfors regular measures; however, a thorough analysis of these structures has not been carried out. We present a variety of results on these spaces including their basic functional properties, their relations to customary function spaces and mutual embeddings, and, in a particular situation, a characterization of their associate structures. We discover a new one-parameter path of function spaces leading from a Lebesgue space to a Zygmund class and we compare it to the classical one. |
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Keywords: | embeddings Lorentz–Zygmund spaces maximal nonincreasing rearrangement rearrangement-invariant spaces |
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