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Volume 39, Issue 2
Operators on Sobolev Type Spaces

Guangfu Cao & Li He

DOI: 10.4208/cmr.2022-0032

Commun. Math. Res., 39 (2023), pp. 254-286.

Published online: 2023-04

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  • Abstract

In this paper, we introduce the work done on Hardy-Sobolev spaces and Fock-Sobolev spaces and their operators and operator algebras, including the study of boundedness, compactness, Fredholm property, index theory, spectrum and essential spectrum, norm and essential norm, Schatten-p classes, and the $C^∗$ algebras generated by them.

  • Keywords

Hardy-Sobolev space, Fock-Sobolev space, multiplier, composition operator, Toeplitz operator, Hankel operator.

  • AMS Subject Headings

47B35, 47B07, 32A37, 47A10, 30H20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-39-254, author = {Cao , Guangfu and He , Li}, title = {Operators on Sobolev Type Spaces}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {39}, number = {2}, pages = {254--286}, abstract = {

In this paper, we introduce the work done on Hardy-Sobolev spaces and Fock-Sobolev spaces and their operators and operator algebras, including the study of boundedness, compactness, Fredholm property, index theory, spectrum and essential spectrum, norm and essential norm, Schatten-p classes, and the $C^∗$ algebras generated by them.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2022-0032}, url = {http://global-sci.org/intro/article_detail/cmr/21547.html} }
TY - JOUR T1 - Operators on Sobolev Type Spaces AU - Cao , Guangfu AU - He , Li JO - Communications in Mathematical Research VL - 2 SP - 254 EP - 286 PY - 2023 DA - 2023/04 SN - 39 DO - http://doi.org/10.4208/cmr.2022-0032 UR - https://global-sci.org/intro/article_detail/cmr/21547.html KW - Hardy-Sobolev space, Fock-Sobolev space, multiplier, composition operator, Toeplitz operator, Hankel operator. AB -

In this paper, we introduce the work done on Hardy-Sobolev spaces and Fock-Sobolev spaces and their operators and operator algebras, including the study of boundedness, compactness, Fredholm property, index theory, spectrum and essential spectrum, norm and essential norm, Schatten-p classes, and the $C^∗$ algebras generated by them.

Guangfu Cao & Li He. (2023). Operators on Sobolev Type Spaces. Communications in Mathematical Research . 39 (2). 254-286. doi:10.4208/cmr.2022-0032
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