Reduction theorems for Sobolev embeddings into the spaces of Hölder,Morrey and Campanato type |
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| Authors: | Miloslav Holík |
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| Affiliation: | Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Czech Republic |
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| Abstract: | Let X be a rearrangement‐invariant Banach function space on Q where Q is a cube in  and let  be the Sobolev space of real‐valued weakly differentiable functions f satisfying  . We establish a reduction theorem for an embedding of the Sobolev space  into spaces of Campanato, Morrey and Hölder type. As a result we obtain a new characterization of such embeddings in terms of boundedness of a certain one‐dimensional integral operator on representation spaces. |
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| Keywords: | Rearrangement‐invariant function spaces reduction operator Sobolev embeddings generalized Campanato Morrey and Hö lder spaces Pó lya– Szegö principle 46E30 46E35 |
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