Taiwanese Journal of Mathematics

MICRO-LOCAL STRUCTURE AND TWO KINDS OF WAVELET CHARACTERIZATIONS ABOUT THE GENERALIZED HARDY SPACES

Tao Qian and Qi-Xiang Yang

Full-text: Open access

Abstract

In this paper, we prove two kinds of wavelet characterizations of the predual spaces of the Morrey spaces through considering some micro-local quantities of the predual spaces.

Article information

Source
Taiwanese J. Math., Volume 17, Number 3 (2013), 1039-1054.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499705998

Digital Object Identifier
doi:10.11650/tjm.17.2013.2545

Mathematical Reviews number (MathSciNet)
MR3072276

Zentralblatt MATH identifier
1284.42048

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 30H25: Besov spaces and $Q_p$-spaces

Keywords
generalized Hardy spaces micro-local structure wavelet characterization

Citation

Qian, Tao; Yang, Qi-Xiang. MICRO-LOCAL STRUCTURE AND TWO KINDS OF WAVELET CHARACTERIZATIONS ABOUT THE GENERALIZED HARDY SPACES. Taiwanese J. Math. 17 (2013), no. 3, 1039--1054. doi:10.11650/tjm.17.2013.2545. https://projecteuclid.org/euclid.twjm/1499705998


Export citation

References

  • R. Aulaskari, J. Xiao and R. H. Zhao, On subspaces and subsets of BMOA and UBC, Analysis, 15 (1995), 101-121.
  • L. Carleson, An explicit unconditional basis in $H^1$, Bull. des Sciences Math., 164 (1980), 405-416.
  • L. H. Cui and Q. X. Yang, On the generalized Morrey spaces, Siberian Mathematical Journal, 46(1) (2005), 133-141.
  • L. H. Cui, Q. X. Yang and Z. X. Cheng, Notes on generalized $Q$ spaces (Chinese), Acta Math. Sinica $($Chin. Ser.$)$, 47(2) (2004), 265-272.
  • G. Dafni and J. Xiao, Some new tent spaces and duality theorem for fractional Carleson measures and $Q_{\alpha}(\mathbb{R})^{n}$, J. Funct. Anal., 208 (2004), 377-422.
  • M. Essen, S. Janson, L. Z. Peng and J. Xiao, Q spaces of several real variables, Indiana University mathematics Journal, 2 (2000), 575-615.
  • C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math., 129 (1972), 107-115.
  • S. Janson, On the space $Q_{p}$ and its dyadic counterpart, Proc. Symposium “Complex Analysis and Differential equations", C. Kiselman, ed., June 15-18, 1997, Uppsala, Sweden, Acta Universitatis Upsaliensis C., 64 (1999), 194-205.
  • F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math., 14 (1961), 415-426.
  • E. A. Kalita, Dual Morrey spaces, Dokl. Akad. Nauk, 361 (1998), 447-449.
  • C. Lin and Q. Yang, Semigroup characterization of Besov type Morrey spaces and well-posedness of generalized Navier-Stokes equations, J. Differential Equations, 254 (2013), 804-846.
  • B. Maurey, Isomorphismes entre espaces $H^1$, Acta Math., 145 (1980), 79-120.
  • Y. Meyer, Ondelettes et Opérateurs, I et II, Hermann, Paris, 1991-1992.
  • Y. Meyer and Q. X. Yang, Continuity of Calderón-Zygmund operators on Besov or Triebel-Lizorkin spaces, Anal. Appl. $($Singap.$)$, 6(1) (2008), 51-81.
  • C. B. Morrey, On the solutions of quasi-linear elliptic partial differential equations, Trans Amer. Math. Soc., 43(1) (1938), 126-166.
  • L. Z. Peng and Q. X. Yang, Predual spaces for $Q$ spaces, Acta Math. Sci. Ser. B Engl. Ed., 29(2) (2009), 243-250.
  • Y. Sawano, Wavelet characterization of Besov-Morrey and Triebel-Lizorkin-Morreyspaces, Funct. Approx. Comment. Math., 38(part 1) (2008), 93-107.
  • D. A. Stegenga, Bounded Toeplitz operators on $H^{1}$ and Applications of the duality between $H^{1}$ and the functions of bounded mean oscillation, Amer. J. Math., 98(3) (1976), 573-589.
  • E. M. Stein, Harmonic Analysis-real Variable Methods, Orthogonality and Integrals, Princeton University Press, 1993.
  • H. Triebel, Theory of Function Spaces, Birkhauser Verlag, Basel, Boston, Stuttgart, 1983.
  • P. Wojtaszczyk, Franklin system is an unconditional basis in $H^1$, Ark. Mat., 20 (1982), 293-300.
  • P. Wojtaszczyk, A Mathematical Introduction to Wavelets, London Mathematical Society Student Texts, 37, Cambridge University Press, 1997.
  • Z. J. Wu and C. P. Xie, Q spaces and Morrey spaces, J. Func. Anal., 201(1) (2003), 282-297.
  • J. Xiao, Homothetic variant of fractional Sobolev space with application to Navier-Stokes system, Dyn. Partial Differ. Equ., 4(3) (2007), 227-245.
  • D. C. Yang and W. Yuan, New Besov-type spaces and TriebelCLizorkin-type spaces including Q spaces, Math. Z., 265 (2010), 451-480.
  • Q. X. Yang, Wavelet and Distribution, Beijing Science and Technology Press, 2002.
  • Q. X. Yang, Characterization of multiplier spaces with Daubechies wavelets, Acta Math. Sci. Ser. B, 32(6) (2012), 2315-2321.
  • Q. X. Yang and F. W. Deng, Wavelet characterization of multiplier spaces, Mathematical Methods in the Applied Sciences, Math. Meth. Appl. Sci., 35 (2012), 2085-2094.
  • Q. X. Yang, Z. X. Chen and L. Z. Peng, Uniform characterization of function spaces by wavelets, Acta Math. Sci. Ser. A, 25(1) (2005), 130-144.
  • Q. X. Yang and Y. P. Zhu, Generalized Morrey spaces, multiplier spaces and stability, submited.
  • Q. X. Yang and Y. P. Zhu, Characterization of multiplier spaces by wavelets and logarithmic Morrey spaces, Nonlinear Anal., 75(13) (2012), 4920-4935.
  • W. Yuan, W. Sickel and D. C. Yang, Morrey and Campanato Meet Besov, Lizorkin and Triebel, Lecture Notes in Mathematics, 2005, J.-M. Morel, Cachan F. Takens and Groningen B. Teissier, eds., Paris, 2010.