| Title:
|
Singular integral characterization of nonisotropic generalized BMO spaces (English) |
| Author:
|
Crescimbeni, Raquel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
225-238 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We extend a result of Coifman and Dahlberg [{\it Singular integral characterizations of nonisotropic $H^p$ spaces and the F. and M. Riesz theorem\/}, Proc. Sympos. Pure Math., Vol. 35, pp.\,231--234; Amer. Math. Soc., Providence, 1979] on the characterization of $H^p$ spaces by singular integrals of $\Bbb R^n$ with a nonisotropic metric. Then we apply it to produce singular integral versions of generalized BMO spaces. More precisely, if $T_\lambda$ is the family of dilations in $\Bbb R^n$ induced by a matrix with a nonnegative eigenvalue, then there exist $2n$ singular integral operators homogeneous with respect to the dilations $T_\lambda$ that characterize BMO$_\varphi$ under a natural condition on $\varphi$. (English) |
| Keyword:
|
singular integral |
| Keyword:
|
nonisotropic generalized BMO |
| MSC:
|
42B30 |
| MSC:
|
42B99 |
| MSC:
|
46E15 |
| idZBL:
|
Zbl 1199.42112 |
| idMR:
|
MR2338091 |
| . |
| Date available:
|
2009-05-05T17:02:31Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119653 |
| . |
| Reference:
|
[CD] Coifman R., Dahlberg B.: Singular integral characterizations of nonisotropic $H^p$ spaces and the F. and M. Riesz theorem.Proc. Sympos. Pure Math., Vol. 35, pp.231-234; Amer. Math. Soc., Providence, 1979. MR 0545260 |
| Reference:
|
[CW] Coifman R., Weiss G.: Analyse harmonique non-conmutative sur certain espaces homogenes.Lecture Notes in Mathematics 242, Springer, Berlin-New York, 1971. MR 0499948 |
| Reference:
|
[C] Crescimbeni R.: Singular integral characterization of functions with conditions on the mean oscillation on spaces of homogeneous type.Rev. Un. Mat. Argentina 39 153-171 (1995). Zbl 0892.42007, MR 1376792 |
| Reference:
|
[FS] Fefferman C., Stein E.: $H^p$ spaces of several variables.Acta Math. 129 137-193 (1972). MR 0447953 |
| Reference:
|
[G] de Guzmán M.: Real Variable Methods in Fourier Analysis.Mathematics Studies 46, North Holland, Amsterdam, 1981. MR 0596037 |
| Reference:
|
[KR] Krasnosel'skii M., Rutickii J.: Convex Functions and Orlicz Spaces.Noordhoff, Groningen, 1961. MR 0126722 |
| Reference:
|
[MS1] Macías R., Segovia C.: Lipschitz functions on spaces of homogeneous type.Adv. in Math. 33 257-270 (1979). MR 0546295 |
| Reference:
|
[MS2] Macías R., Segovia C.: A decomposition into atoms of distributions on spaces of homogeneous type.Adv. in Math. 33 271-309 (1979). MR 0546296 |
| Reference:
|
[V] Viviani B.: An atomic decomposition of the predual of ${BMO} (\rho)$.Rev. Mat. Iberoamericana 3 3-4 401-425 (1987). Zbl 0665.46022, MR 0996824 |
| . |
