Sobolev spaces on canonical Banach spaces and Fourier transformations
DOI:
https://doi.org/10.5269/bspm.70666Resumen
In this article, Sobolev spaces on canonical Banach spaces has been discussed. The Hilbert structure of the Sobolev spaces are discussed in this settings. Finally, in application, we discuss the Fourier transform and its relevance for Sobolev spaces on canonical Banach spaces.
Referencias
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2. T.L. Gill, W.W. Zachary, Functional Analysis and Feynman Operator Calculus, Springer, (2016).
3. T.L. Gill, H. Kalita, B. Hazarika, A family of Banach spaces over R∞, Proc. Singapore National Academy of Science, 15(1)(2021), 9-15
4. J. Heinonen. Nonsmooth calculus. Bull. Am. Math. Soc., New Ser., 44(2), (2007), 163-232, .
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11. P. Haj lasz, P. Koskela. Sobolev met Poincar´e., Providence, RI:, American Mathematical Society, 688, (2000).
12. Jeffrey Rauch, Partial Differential Equations, Springer-Verlag, 1, (1991).
2. T.L. Gill, W.W. Zachary, Functional Analysis and Feynman Operator Calculus, Springer, (2016).
3. T.L. Gill, H. Kalita, B. Hazarika, A family of Banach spaces over R∞, Proc. Singapore National Academy of Science, 15(1)(2021), 9-15
4. J. Heinonen. Nonsmooth calculus. Bull. Am. Math. Soc., New Ser., 44(2), (2007), 163-232, .
5. J. Heinonen, P. Koskela, N. Shanmugalingam, and J. T. Tyson. Sobolev classes of Banach space-valued functions and quasiconformal mappings. J. Anal. Math., 85 (2001) 87-139.
6. J. Heinonen, P. Koskela, N. Shanmugalingam, J. T. Tyson, Sobolev spaces on metric measure spaces. An approach based on upper gradients., Cambridge: Cambridge University Press, 27, (2015).
7. J. Kinnunen, Sobolev Spaces Department of Mathematics and Systems Analysis, Aalto University (2017).
8. H. Kalita, B. Hazarika, T. Myres, Kuelbs-Steadman spaces on separable Banach spaces, facta Universitatis (NIS) Ser. Math. Inform. Vol. 36, No 5 (2021), 1065-1077
9. J. Kuelbs, Gaussian measures on a Banach space, J. Funct. Anal. 5(1970), 354-367.
10. G. Leoni, A first course in Sobolev spaces, AMS Graduate studies in Mathematics, Vol. 105, American Mathematical Society, Providence, RI, (2009).
11. P. Haj lasz, P. Koskela. Sobolev met Poincar´e., Providence, RI:, American Mathematical Society, 688, (2000).
12. Jeffrey Rauch, Partial Differential Equations, Springer-Verlag, 1, (1991).
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Publicado
2025-09-02
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Research Articles
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