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MAPPING PROPERTIES OF THE MARCINKIEWICZ INTEGRALS ON HOMOGENEOUS GROUPS
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 Title & Authors
MAPPING PROPERTIES OF THE MARCINKIEWICZ INTEGRALS ON HOMOGENEOUS GROUPS
Choi, Young-Woo; Rim, Kyung-Soo;
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 Abstract
Under the cancellation property and the Lipschitz condition on kernels, we prove that the Marcinkiewicz integrals defined on a homogeneous group H are bounded from (H) to (H), from (H) to BMO (H), and from (H) to (H) for 1 < p < assuming the -boundedness for some q > 1.for some q > 1.
 Keywords
Marcinkiewicz integrals;homogeneous groups;
 Language
English
 Cited by
 References
1.
A. Benedek, A. Calderon, and R. Panzone, Convolution operators on Banach space valued functions, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 356-365 crossref(new window)

2.
A. P. Calderon, On the theorem of Marcinkiewicz and Zygmund, Trans. Amer. Math. Soc. 68 (1950), 55-61. crossref(new window)

3.
A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85-139 crossref(new window)

4.
J. Duoandikoetxea and J. L. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), 541-561. crossref(new window)

5.
C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), 137-193 crossref(new window)

6.
G. B. Folland and E. M. Stein, Hardy spaces on homogeneous groups, Princeton Univ. Press, 1982

7.
J. Marcinkiewicz, Sur quelques integrales de type de Dini, Annales de la Société Polonaise 17 (1938), 42-50

8.
E. M. Stein, On the function of Littlewood-Paley, Lusin and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958), 430-466 crossref(new window)

9.
E. M. Stein, Singular integrals and differeniability properties of functions, Princeton Univ. Press, 1970

10.
E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, 1993

11.
E. M. Stein and G. Weiss, On the interpolation of analytic families of operators acting on $H^{p}$ spaces, Tôhoku Math. J. 9 (1957), 318-339. crossref(new window)

12.
A. Torchinsky, Real-variable methods in harmonic analysis, Academic Press, 1986

13.
A. Torchinsky and S. Wang, A note on the Marcinkiewicz integral, Colloq. Math. 61-62 (1990), 235-243.

14.
A. Zygmund, On certain integrals, Trans. Amer. Math. Soc. 55 (1944), 170-204 crossref(new window)

15.
A. Zygmund, Trigonometric Series, 2nd ed. Vol. 2, Cambridge Univ. Press, Cambridge, 1968.