Hardy spaces Hp and BMO: A brief clasicc overview


  • Alejandro Ortiz Fernández Sección Matemática. Pontificia Universidad Católica del Perú, Lima, Perú.




BMO, H^p, BMO_varphi, operator, H^{p,q}, duality, (p,q)-atom


In this brief note we give an overview of Hardy spaces Hp and bounded mean oscillation spaces, BMO, two classic spaces that have played an important role in investigations of central branches in harmonic analysis. The given bibliography opens paths to follow in this field.


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Calderón AP, Torchinsky A. Parabolical maximal functions associated with a distribution. Adv. in Math. 1975; 16(1):1-63.

Campanato S. Propietá di una famiglia di spazi funcionali. Ann. S. N. S. di Pisa. 3 serie, 1964; 18(1):137-160.

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Campanato S. Equazioni elliptiche del II° ordine espazi $mathscr{L}^{(2,lambda)}$. Ann. Mat. Pura Appl, 1965; 69:321-380.

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Coifman R, Weiss G. Extension of Hardy spaces and their use in analysis. Bull. Am. Math.S. 1977; 83(4):569-646.

Coifman R, Weiss G. Anayse harmonique non-commutative sur certains spaces homogenes. Berlin-New York: Springer-Verlag. Vol. 242. 1971.

Fabes EB, Jhonson RL, Neri U. Spaces of harmonic functions representable by Poisson integrals of fuctions in BMO and L^p,lambda}. Ind. Univ. Math.J. 1976; 25(2):159-170.

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García-Cuerva J. Rubio de Francia J. Weighted norm in equalities and related topics. N. York: North-Holland, 1985.

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Janson, S. Mean oscillation and conmutators of singulatar integral operators. Archiv der Math. 1978: 16:263-270.

John F, Nirenberg L. On functions of bounded mean oscillation. Comm. P. Appl. Match. 1961; XIV:415-426.

Latter R. A descomsition of H^p (Rn{n}) in terms of atoms. Studia Math. 1977: 92-101.

Macias R. Interpolation theorems on generalized Hardy spaces. Ph.D. Thesis. Washington Univ. 1974.

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Macías R, Segovia C. Lipschitz functions on spaces of homogeneous type. Adv. in Math. 1979; 33(3):257-270.

Macías R, Segovia C. A maximal theory of general Hardy spaces. Proc. of Symp. in pure Math. 1979.

Muckenhoupt B, Weeden R. Weighted bounded mean oscillation and the Hilbert transform. Studia Math. 1976; 54(3):221-237.

Neri U. Fractional integration on the space H^1 and its dual. Studia Math. 1975. LII:176-189.

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Sadosky C. Interpolation of operators and singular integrals. Marcel Dekker. 1979.

Spanne S. Some function spaces defined using the mean oscillation over cubes. Ann. Sc. Sup. di Pisa er Serie. 1965; 19(4):593-608.

Stampacchia G. The L^{p,lambda} spaces and application to the theory of partial differential equations. Proc. Cong. Diff. Eq. and Appli. 1969.

Stegenga DA. Bounded mean oscillation on pseudometric space. Pre - preprint.

Stein EM. Harmonic analysis: Real - variable methods, orthogonality, and oscillatory integrals. Pricenton. N.J.: Princenton University Press. 1993.

Strömberg J-O, Torchinsky A. Weighted Hardy Spaces. Springer-Verlag. 1989.

Torchinsky A. Real-Variable Methods in Harmonic Analysis. N.York: Academic Press, INC. 1986.

Zhu K. Operator theory in fuction spaces. Marcel Dekker, Inc. N.Y. 1990.

Ortiz JA, Torchinsky A. On a mean value inequality. Indiana U. Math. J. 1977; 26(3):555-566.



How to Cite

Ortiz Fernández, A. . (2022). Hardy spaces Hp and BMO: A brief clasicc overview . Selecciones Matemáticas, 9(02), 381 - 394. https://doi.org/10.17268/sel.mat.2022.02.13

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