|
Hardy spaces and partial derivatives of conjugate harmonic functions
Author(s):
Anatoly
Ryabogin;
Dmitry
Ryabogin
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2461-2470.
MSC (2000):
Primary 30E25;
Secondary 42B25
Posted:
April 5, 2007
MathSciNet review:
2302567
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we give necessary and sufficient conditions for a harmonic vector and all its partial derivatives to belong to for all .
References:
-
- 1.
- A. A. Bonami, Integral inequalities for conjugate harmonic functions of several variables, Math. Sbornik, Vol. 87 129 (1972), No. 2, pp. 188-203. MR 0299818 (45:8866)
- 2.
- D. L. Burkholder, R. V. Gundy and M. L. Silverstein, A maximal function characterization of the class
, Trans. AMS., 157 (1971), 137-153. MR 0274767 (43:527) - 3.
- A. P. Calderón and A. Zygmund, On higher gradients of harmonic functions, Studia Math. 24 (1964), No. 2, 211-266. MR 0167631 (29:4903)
- 4.
- C. Fefferman and E. M. Stein,
spaces of several variables, Acta Math., 129, No. 3, (1972), 137-193. MR 0447953 (56:6263) - 5.
- T. M. Flett, Inequalities for the
-th mean values of harmonic and subharmonic functions with , Proc. London Math. Soc., Ser. 3, 20, No. 3, (1970), 249-275. MR 0257387 (41:2038) - 6.
- V. I. Krylov, On functions regular in the half-plane, Math., Sb., (1939), 6 (48), pp.95-138.
- 7.
- U. Kuran, Classes of subharmonic functions in
, Proc. London Math. Soc., Ser. 3, 16 (1966), No. 3, 473-492. MR 0203059 (34:2917) - 8.
- I. Privalov, Subharmonic functions, Moscow, 1937.
- 9.
- A. Ryabogin, Conjugate harmonic functions of the Hardy class. (Russian), Izv. Vyssh. Uchebn. Zaved. Mat. 1991, , no. 9, 47-53; translation in Soviet Math. (Iz. VUZ) 35 (1991), no. 9, 46-51. MR 1169391 (93e:42033)
- 10.
- A. Ryabogin, Boundary values of conjugate harmonic functions of several variables, (Russian), Izv. Vyssh. Uchebn. Zaved. Mat. (1980), no. 12, 50-54. MR 606677 (82d:31007)
- 11.
- E. D. Solomentsev, On classes of subharmonic functions in the half-space, Notes of Moscow State Univ., 10, (1958).
- 12.
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, Princeton NJ, 1970. MR 0290095 (44:7280)
- 13.
- E. M. Stein and G. Weiss, On the theory of harmonic functions of several variables, Acta Math., 103 (1960), pp. 26-62. MR 0121579 (22:12315)
- 14.
- E. M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representation of the rotation group, Amer. J. Math., 90 (1968), 163-196. MR 0223492 (36:6540)
- 15.
- E. M. Stein and G. Weiss, An introduction to harmonic analysis on Euclidean spaces, Princeton University Press, Princeton NJ, 1969.
- 16.
- T. Wolff, Counterexamples with harmonic gradient in
, Essays in honor of E. M. Stein, Princeton Mathematical Series, 42 (1995), 321-384. MR 1315554 (95m:31010) - 17.
- A. Zygmund, Trigonometric series, 2nd ed., Cambridge University Press, Cambridge, 1968. MR 0236587 (38:4882)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
30E25,
42B25
Retrieve articles in all Journals with
MSC (2000):
30E25,
42B25
Additional Information:
Anatoly
Ryabogin
Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be'er Sheva 84105, Israel
Email:
ryabs@math.ksu.edu
Dmitry
Ryabogin
Affiliation:
Department of Mathematics, Kansas State University, Manhattan, Kansas 66506-2602
Email:
ryabs@math.ksu.edu
DOI:
10.1090/S0002-9939-07-08940-X
PII:
S 0002-9939(07)08940-X
Keywords:
Hardy spaces,
subharmonic functions
Received by editor(s):
January 31, 2006
Posted:
April 5, 2007
Communicated by:
Mei-Chi Shaw
Copyright of article:
Copyright
2007,
American Mathematical Society
|