The atomic decomposition for parabolic 𝐻^{𝑝} spaces

Latter, Robert H.; Uchiyama, Akihito

doi:10.1090/S0002-9947-1979-0536954-6

The atomic decomposition for parabolic $H^{p}$ spaces
HTML articles powered by AMS MathViewer

by Robert H. Latter and Akihito Uchiyama PDF

Trans. Amer. Math. Soc. 253 (1979), 391-398 Request permission

Abstract:

The theorem of A. P. Calderón giving the atomic decomposition for certain parabolic ${H^p}$ spaces is extended to all such spaces. The proof given also applies to Hardy spaces defined on the Heisenberg group.

References

Alberto-P. Calderón, An atomic decomposition of distributions in parabolic $H^{p}$ spaces, Advances in Math. 25 (1977), no. 3, 216–225. MR 448066, DOI 10.1016/0001-8708(77)90074-3
A.-P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution, Advances in Math. 16 (1975), 1–64. MR 417687, DOI 10.1016/0001-8708(75)90099-7
A.-P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution. II, Advances in Math. 24 (1977), no. 2, 101–171. MR 450888, DOI 10.1016/S0001-8708(77)80016-9
Ronald R. Coifman, A real variable characterization of $H^{p}$, Studia Math. 51 (1974), 269–274. MR 358318, DOI 10.4064/sm-51-3-269-274
Ronald R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645. MR 447954, DOI 10.1090/S0002-9904-1977-14325-5
C. Fefferman, N. M. Rivière, and Y. Sagher, Interpolation between $H^{p}$ spaces: the real method, Trans. Amer. Math. Soc. 191 (1974), 75–81. MR 388072, DOI 10.1090/S0002-9947-1974-0388072-3
John B. Garnett and Robert H. Latter, The atomic decomposition for Hardy spaces in several complex variables, Duke Math. J. 45 (1978), no. 4, 815–845. MR 518108
Daryl Geller, Fourier analysis on the Heisenberg group. I. Schwartz space, J. Functional Analysis 36 (1980), no. 2, 205–254. MR 569254, DOI 10.1016/0022-1236(80)90100-7

Generalized function spaces of Campanato type

Adam Korányi, Harmonic functions on Hermitian hyperbolic space, Trans. Amer. Math. Soc. 135 (1969), 507–516. MR 277747, DOI 10.1090/S0002-9947-1969-0277747-0
A. Korányi and S. Vági, Singular integrals on homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 25 (1971), 575–648 (1972). MR 463513
Robert H. Latter, A characterization of $H^{p}(\textbf {R}^{n})$ in terms of atoms, Studia Math. 62 (1978), no. 1, 93–101. MR 482111, DOI 10.4064/sm-62-1-93-101
Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095