Publication:
Compactness interpolation results for bilinear operators of convolution type and for operators of product type

Loading...
Thumbnail Image
Full text at PDC
Publication Date
2022
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
We establish compactness interpolation results for bilinear operators of convolution type and for operators of product type among quasi-Banach spaces. We do not assume any auxiliary condition on the spaces.
Description
CRUE-CSIC (Acuerdos Transformativos 2021)
Unesco subjects
Keywords
Citation
[1] T. Aoki, Locally bounded linear topological maps, Proc. Imp. Acad. Tokyo 18 (1942) 588-594. [2] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston, 1988. [3] Á. Bényi and R.H. Torres, Compact bilinear operators and commutators, Proc. Amer. Math. Soc. 141 (2013) 3609-3621. [4] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976. [5] B.F. Besoy and F. Cobos, Interpolation of the measure of non-compactness of bilinear operators among quasi-Banach spaces, J. Approx. Theory 243 (2019) 25-44. [6] A.P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964) 113-190. [7] F. Cobos, D.E. Edmunds and A.J.B. Potter, Real interpolation and compact linear operators, J. Funct. Anal. 88 (1990) 351-365. [8] F. Cobos, L.M. Fernández-Cabrera and A. Martínez, Interpolation of compact bilinear operators among quasi-Banach spaces and applications, Math. Nachr. 291 (2018) 2168-2187. [9] F. Cobos, L.M. Fernández-Cabrera and A. Martínez, On compactness results of Lions-Peetre type for bilinear operators, Nonlinear Anal. 199 (2020) 111951. [10] F. Cobos, L.M. Fernández-Cabrera and A. Martínez, A compactness result of Janson type for bilinear operators, J. Math. Anal. Appl. 495 (2021) 124760. [11] F. Cobos, L.M. Fernández-Cabrera and A. Martínez, On the interpolation of the measure of non-compactness of bilinear operators with weak assumptions on the boundedness of the operator, J. Math. Anal. Appl. 504 (2021) 125376. [12] F. Cobos, T. Kühn and T. Schonbek, One-sided compactness results for Aronszajn-Gagliardo functors, J. Funct. Anal. 106 (1992) 274-313. [13] F. Cobos and J. Peetre, Interpolation of compactness using Aronszajn-Gagliardo functors, Israel J. Math. 68 (1989) 220-240. [14] D.E. Edmunds and W.D. Evans, Hardy Operators, Function Spaces and Embeddings, Springer, Berlin, 2004. [15] D.E. Edmunds and H. Triebel, Function Spaces, Entropy Numbers and Differential Operators, Cambridge Univ. Press, Cambridge, 1996. [16] D.L. Fernandez and E.B. da Silva, Interpolation of bilinear operators and compactness, Nonlinear Anal. 73 (2010) 526-537. [17] L.M. Fernández-Cabrera and A. Martínez, On interpolation properties of compact bilinear operators, Math. Nachr. 290 (2017) 1663-1677. [18] L.M. Fernández-Cabrera and A. Martínez, Real interpolation of compact bilinear operators, J. Fourier Anal. Appl. 24 (2018) 1181-1203. [19] J.E. Gilbert and A.R. Nahmod, Hardy spaces and a Walsh model for bilinear cone operators, Trans. Amer. Math. Soc. 351 (1999) 3267-3300. [20] S. Janson, On interpolation of multilinear operators, in: Function spaces and Applications, in: Springer Lect. Notes in Math., vol. 1302, 1988, pp. 290-302. [21] G.E. Karadzhov, The interpolation method of "means" for quasinormed spaces, Doklady Acad. Nauk SSSR 209 (1973) 33-36. [22] H. König, Interpolation of operator ideals with an application to eigenvalue distribution problems, Math. Ann. 233 (1978) 35-48. [23] H. König, Eigenvalue Distribution of Compact Operators, Birkhäuser, Basel, 1986. [24] G. Köthe, Topological Vector Spaces I, Springer, Berlin, 1969. [25] P. Krée, Interpolation d'espaces vectoriels qui ne sont ni normés, ni complets. Applications, Ann. Inst. Fourier 17 (1967) 137-174. [26] J.-L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math. 19 (1964) 5-68. [27] M. Mastylo and E.B. Silva, Interpolation of the measure of non-compactness of bilinear operators, Trans. Amer. Math. Soc. 370 (2018) 8979-8997. [28] M. Mastylo and E.B. Silva, Interpolation of compact bilinear operators, Bull. Math. Sci. 10 (2020) 2050002. [29] R. O'Neil, Convolution operators and L(p; q) spaces, Duke Math. J. 30 (1963) 129-142. [30] J. Peetre, Paracommutators and minimal spaces, in: Operators and Function Theory, ed. S.C. Power, Reidel, Boston, 1985. [31] S. Rolewicz, On a certain class of linear metric spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astrono. Phys. 5 (1957) 471-473. [32] R. Sharpley, Multilinear weak type interpolation of mn-tuples with applications, Studia Math. 60 (1977) 179-194. [33] R.H. Torres, Q.Y. Xue and J. Yan, Compact bilinear commutators: the quasi-Banach space case, J. Anal. 26 (2018) 227-234. [34] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. [35] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983.
Collections