Abstract
In this paper, we give optimal embedding relations between local Hardy spaces and α-modulation spaces. By a different approach, we extend the main results obtained by Kobayashi, Miyachi and Tomita in [Studia Math., 192 (2009), 79–96].
Similar content being viewed by others
References
L. Borup and M. Nielsen, Banach frames for multivariate α-modulation spaces, J. Math. Anal. Appl., 321 (2006), 880–895.
H. G. Feichtinger, Modulation spaces on locally compact Abelian groups, in: Proc. Internat. Conf. on Wavelet and Applications, New Delhi Allied Publishers (India, 2003), pp. 99–140.
H. G. Feichtinger, Modulation spaces: looking back and ahead, Sampl. Theory Signal Image Process., 5 (2006), 109–140.
H. G. Feichtinger and P. Gröbner, Banach spaces of distributions defined by decomposition methods. I, Math. Nachr., 123 (1985), 97–120.
M. Fornasier, Banach frames for α-modulation spaces, Appl. Comput. Harmon. Anal., 22 (2007), 157–175.
D. Goldberg, A local version of real Hardy spaces, Duke Math. J., 46 (1979), 27–42.
P. Gröbner, Banachräume Glatter Funktionen and Zerlegungsmethoden, Doctoral Thesis, University of Vienna (1992).
K. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser (Boston, MA, 2001).
W. Guo and J. Chen, Strichartz estimates on α-modulation spaces, Electron. J. Differential Equations, 118 (2013), 1–13.
W. Guo, D. Fan, H. Wu and G. Zhao, Sharpness of complex interpolation on α-modulation spaces, J. Fourier Anal. Appl.,22 (2016), 1–35.
W. Guo, H. Wu and G. Zhao, Inclusion relations between modulation and Triebel-Lizorkin spaces, Proc. Amer. Math. Soc., 145 (2017), 4807–4820.
W. Guo, D. Fan and G. Zhao, Full characterization of embedding relations between α-modulation spaces, Sci. China Math., 61 (2018), 1243–1272.
J. Han and B. Wang, α-modulation spaces. (I) embedding, interpolation and algebra properties, J. Math. Soc. Japan, 66 (2014), 1315–1373.
T. Kato, On modulation spaces and their applications to dispersive equations, Doctoral Thesis (2016).
T. Kato, The inclusion relations between α-modulation spaces and Lp-Sobolev spaces or local Hardy spaces, J. Funct. Anal., 272 (2017), 1340–1405.
M. Kobayashi, A. Miyachi and N. Tomita, Embedding relations between local Hardy and modulation spaces, Studia Math., 192 (2009), 79–96.
M. Kobayashi and M. Sugimoto, The inclusion relation between Sobolev and modulation spaces, J. Funct. Anal., 260 (2011), 3189–3208.
M. Nielsen, Orthonormal bases for α-modulation spaces, Collect. Math., 61 (2010), 173–190.
K. Okoudjou, Embeddings of some classical Banach spaces into modulation spaces, Proc. Amer. Math. Soc., 132 (2004), 1639–1647.
M. Sugimoto and N. Tomita, The dilation property of modulation space and their inclusion relation with Besov spaces, J. Funct. Anal., 248 (2007), 79–106.
J. Toft, Continuity properties for modulation spaces, with applications to pseudo-differential calculus. I, J. Funct. Anal., 207 (2004), 399–429.
J. Toft and P. Wahlberg, Embeddings of α-modulation spaces, Pliska Stud. Math. Bulgar., 21 (2012), 25–46.
H. Triebel, Modulation spaces on the euclidean n-space, Z. Anal. Anwend., 2 (1983), 443–457.
H. Triebel, Theory of Function Spaces. II, Birkhäuser (Basel, 1992).
M. Ruzhansky, M. Sugimoto and B. Wang, Modulation spaces and nonlinear evolution equations, Progr. Math., 301 (2012), 267–283.
F. Voigtlaender, Embedding theorems for decomposition spaces with applications to wavelet coorbit spaces, Doctoral Thesis, RWTH Aachen University (2016).
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the National Natural Science Foundation of China (Grants 11701112, 11701130, 11671414 and 11601456), and the Natural Science Foundation of Fujian Province (Grants 2020J01267, 2020J01708).
Rights and permissions
About this article
Cite this article
Zhao, G., Gao, G. & Guo, W. Sharp Embedding Relations Between Local Hardy and α-Modulation Spaces. Anal Math 47, 451–481 (2021). https://doi.org/10.1007/s10476-021-0077-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10476-021-0077-7