JOURNAL BROWSE
Search
Advanced SearchSearch Tips
CONTINUOUS CHARACTERIZATION OF THE TRIEBEL-LIZORKIN SPACES AND FOURIER MULTIPLIERS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
CONTINUOUS CHARACTERIZATION OF THE TRIEBEL-LIZORKIN SPACES AND FOURIER MULTIPLIERS
Cho, Yong-Kum;
  PDF(new window)
 Abstract
We give a set of continuous characterizations for the homogeneous Triebel-Lizorkin spaces and use them to study boundedness properties of Fourier multiplier operators whose symbols satisfy a generalization of Hrmander`s condition. As an application, we give new direct proofs of the imbedding theorems of the Sobolev type.
 Keywords
Fourier multiplier;Sobolev imbedding;Triebel-Lizorkin spaces;Besov-Lipschitz spaces;singular integrals;
 Language
English
 Cited by
1.
Fourier Multipliers on Triebel-Lizorkin-Type Spaces, Journal of Function Spaces and Applications, 2012, 2012, 1  crossref(new windwow)
2.
Musielak–Orlicz Besov-type and Triebel–Lizorkin-type spaces, Revista Matemática Complutense, 2014, 27, 1, 93  crossref(new windwow)
3.
Equivalent Quasi-Norms of Besov–Triebel–Lizorkin-Type Spaces via Derivatives, Results in Mathematics, 2017, 72, 1-2, 813  crossref(new windwow)
4.
Function spaces of Besov-type and Triebel-Lizorkin-type — a survey, Applied Mathematics-A Journal of Chinese Universities, 2013, 28, 4, 405  crossref(new windwow)
 References
1.
H.-Q. Bui, M. Paluszynski, and M. Taibleson, A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces, Studia Math. 119 (1996), no. 3, 219–246.

2.
H.-Q. Bui, M. Paluszynski, and M. Taibleson, Characterization of the Besov-Lipschitz and Triebel-Lizorkin spaces. The case q < 1, J. Fourier Anal. Appl. 3 (1997), Special Issue, 837–846.

3.
H.-Q. Bui and M. Taibleson, The characterization of the Triebel-Lizorkin spaces for p = ${\infty}$, J. Fourier Anal. Appl. 6 (2000), no. 5, 537–550. crossref(new window)

4.
A. P. Calderon, Lebesgue spaces of differentiable functions and distributions, Proc. Sympos. Pure Math., Vol. IV pp. 33–49 American Mathematical Society, Providence, R.I., 1961.

5.
A. P. Calderon and A. Torchinsky, Parabolic maximal functions associated with a distribution, Advances in Math. 16 (1975), 1–64. crossref(new window)

6.
Y.-K. Cho, Strichartz’s conjecture on Hardy-Sobolev spaces, Colloq. Math. 103 (2005), no. 1, 99–114. crossref(new window)

7.
Y.-K. Cho and J. Kim, Atomic decomposition on Hardy-Sobolev spaces, Studia Math. 177 (2006), no. 1, 25–42. crossref(new window)

8.
C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. crossref(new window)

9.
M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), no. 1, 34–170. crossref(new window)

10.
M. Frazier, B. Jawerth, and G. Weiss, Littlewood-Paley Theory and the Study of Function Spaces, CBMS Regional Conference Series in Mathematics, 79. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1991.

11.
L. Grafakos, Classical and Modern Fourier Analysis, Pearson Education, Inc., Upper Saddle River, NJ, 2004.

12.
B. Jawerth, Some observations on Besov and Lizorkin-Triebel spaces, Math. Scand. 40 (1977), no. 1, 94–104. crossref(new window)

13.
J. Johnsen and W. Sickel, A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin-Triebel spaces with mixed norms, J. Funct. Spaces Appl. 5 (2007), no. 2, 183–198. crossref(new window)

14.
J. Peetre, On spaces of Triebel-Lizorkin type, Ark. Mat. 13 (1975), 123–130. crossref(new window)

15.
E. M. Stein, Harmonic Analysis : Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993.

16.
R. Strichartz, Bounded mean oscillation and Sobolev spaces, Indiana Univ. Math. J. 29 (1980), no. 4, 539–558. crossref(new window)

17.
R. Strichartz, $H^p$ Sobolev spaces, Colloq. Math. 60/61 (1990), no. 1, 129–139.

18.
H. Triebel, Spaces of distributions of Besov type on Euclidean n-space. Duality, interpolation, Ark. Mat. 11 (1973), 13–64. crossref(new window)

19.
H. Triebel, Theory of Function Spaces, Monographs in Math. 78. Birkhauser Verlag, Basel, 1983.