| Title:
|
The Fourier integral operators on Hardy spaces associated with Herz spaces (English) |
| Author:
|
Liu, Lixia |
| Author:
|
Ma, Bolin |
| Author:
|
Liu, Sanyang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
271-287 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, it is proved that the Fourier integral operators of order $m$, with $-n < m \leq -(n-1)/2$, are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces. (English) |
| Keyword:
|
Fourier integral operator |
| Keyword:
|
Hardy spaces |
| Keyword:
|
Herz spaces |
| MSC:
|
35S30 |
| MSC:
|
42B30 |
| MSC:
|
47B38 |
| MSC:
|
47G10 |
| idZBL:
|
Zbl 1216.47056 |
| idMR:
|
MR2782773 |
| DOI:
|
10.1007/s10587-011-0012-3 |
| . |
| Date available:
|
2011-05-23T12:47:15Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141532 |
| . |
| Reference:
|
[1] Hörmander, L.: Fourier integral operators I.Acta Math. 127 (1971), 79-183. MR 0388463, 10.1007/BF02392052 |
| Reference:
|
[2] Lu, S., Yang, D.: The Littlewood-Paley function and $\phi$-transform characterizations of a new Hardy space $HK_2$ associated with the Herz space.Stud. Math. 101 (1992), 285-298. MR 1153785, 10.4064/sm-101-3-285-298 |
| Reference:
|
[3] Lu, S., Yang, D.: The decomposition of the weighted Herz spaces on $R_n$ and its applications.Sci. China Ser. A 38 (1995), 147-158. MR 1338138 |
| Reference:
|
[4] Lu, S., Yang, D.: The weighted Herz-type Hardy space and its applications.Sci. China Ser. A 38 (1995), 661-673. Zbl 0832.42013, MR 1351232 |
| Reference:
|
[5] Marco, M. P., Silvia, S.: Boundedness of Fourier integral operators on Hardy spaces.Proc. Edinb. Math. Soc. 51 (2008), 443-463. MR 2465918, 10.1017/S001309150500012X |
| Reference:
|
[6] Seeger, A., Sogge, C., Stein, E.: Regularity properties of Fourier integral operators.Ann. Math. 134 (1991), 231-251. Zbl 0754.58037, MR 1127475, 10.2307/2944346 |
| Reference:
|
[7] Stein, E.: Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals.Princeton University Press (1993). Zbl 0821.42001, MR 1232192 |
| Reference:
|
[8] Yang, D.: The real-variable characterizations of Hardy spaces $HK_p(R^n)$.Adv. Math. 24 (1995), 63-73. MR 1334605 |
| Reference:
|
[9] Zhou, Y.: Boundedness of sublinear operators in Herz-type Hardy spaces.Taiwannse J. Math. 13 (2009), 983-996. Zbl 1180.42009, MR 2526352, 10.11650/twjm/1500405453 |
| . |
