On the equivalence between weak BMO and the space of derivatives of the Zygmund class

• Autorzy: Kwessi Eddy

Identyfikatory

DOI

10.1515/dema-2021-0013

• Języki publikacji: EN

Abstrakty

EN

In this paper, we will discuss the space of functions of weak bounded mean oscillation. In particular, we will show that this space is the dual space of the special atom space, whose dual space was already known to be the space of derivative of functions (in the sense of distribution) belonging to the Zygmund class of functions. We show, in particular, that this proves that the Hardy space H1 strictly contains the special atom space.

Słowa kluczowe

EN

BMO; derivative; distributions; Zygmund class

PL

BMO; pochodna; rozkład; przestrzenie Zygmunda

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 140--150
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Kwessi Eddy

• Department of Mathematics, Trinity University, San Antonio, TX, United States of America

Bibliografia

• [1] C. Fefferman, Characterization of bounded mean oscillation, Bull. Amer. Math. Soc. 77(1971), no. 4, 587-588.
• [2] R. Coifman, A real variable characterization of hp, Studia Math. 51(1974), 269-274.
• [3] G. De Souza, Spaces formed by special atoms, PhD thesis, SUNY at Albany, 1980.
• [4] A. Zygmund, Trigonometric Series, Vol. I, II, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2002.
• [5] T. Gill, Banach spaces for the Schwartz distributions, Real Analysis Exchange 43(2017), no. 1, 1-36.
• [6] D. Girela, Analytic functions of bounded mean oscillation, Complex Functions Spaces (Merkrijarvi 1999), Univ. Joensuu Dept. Math. Rep. Ser., 4, 2001, pp. 61-170.
• [7] E. Kwessi, G. De Souza, N. Djitte and M. Ndiaye, The special atom space and Haar wavelets in higher dimensions, Demonstr. Math. 53(2020), 131-151.
• [8] S. Bloom and G. De Souza, Atomic decomposition of generalized Lipschitz spaces, Illinois J. Math. 10(1989), 682-686.
• [9] E. Kwessi and G. De Souza, Analytic characterization of high dimension weighted special atom spaces, Preprint.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).