Integral representation and embedding theorems for n-dimensional multianisotropic spaces with one anisotropic vertex
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We prove embedding theorems for the multianisotropic Sobolev spaces generated by the completely regular Newton polyhedron. Under study is the case of the polyhedron with one anisotropic vertex. We obtain a special integral representation of functions in terms of the tuple of multi-indices of the Newton polyhedron.
Keywordsembedding theorems multianisotropic space completely regular polyhedron integral representation
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- 1.Sobolev S. L., “On one theorem of functional analysis,” Mat. Sb., vol. 4, no. 3, 471–497 (1938).Google Scholar
- 3.Nikol’skiĭ S. M., “On a problem by S. L. Sobolev,” Sib. Mat. Zh., vol. 3, no. 6, 845–857 (1962).Google Scholar
- 9.Karapetyan G. A., “The integral representation and embedding theorems for multianisotropic spaces in the plane with one anisotropic vertex,” Izv. NAN RA Mat., vol. 51, no. 6, 23–42 (2016).Google Scholar
- 10.Karapetyan G. A., “The integral representation and embedding theorems for multianisotropic spaces in the plane,” Izv. NAN RA Mat. (to be published).Google Scholar