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Abstrakty
Our aim is to get characterizations and unconditional bases of variable Sobolev spaces Lp (·),s(Rn) in terms of wavelets. As an application, we obtain the sampling theorem in Lp (·),s(Rn).
Wydawca
Czasopismo
Rocznik
Tom
Strony
37--49
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Department of Mathematics, Faculty of Science, Hokkaido University, Kita 10 Nishi 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan, mitsuo@math.sci.hokudai.ac.jp
Bibliografia
- [1] A. Almeida and S. Samko, Characterization of Riesz and Bessel potentials on variable Lebesgue spaces, J. Fund. Spaces Appl. 4 (2006), 113-144.
- [2] C. Bennet and R. Sharpley, Interpolation of Operators, Academic Press, Boston, San Diego, New York, 1988.
- [3] D. Cruz-Uribe, A. Fiorenza, J. M. Martell and C. Perez, The boundedness of classical operators on variable Lp spaces, Ann. Acad. Sci. Fenn. Math. 31 (2006), 239-264.
- [4] D. Cruz-Uribe, A. Fiorenza and C. J. Neugebauer, The maximal function on variable Lp spaces, Ann. Acad. Sci. Fenn. Math. 28 (2003), 223-238, and ibid. 29 (2004), 247-249.
- [5] L. Diening, Maximal functions on generalized Lebesgue spaces Lp(.), Math. In-equal. Appl. 7 (2004), 245-253.
- [6] L. Diening, Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces. Math. Nachr. 268 (2004), 31-43.
- [7] L. Diening, Maximal functions on Musielak-Orlicz spaces and generalized Lebesgue spaces. Bull. Sci. Math. 129 (2005), 657-700.
- [8] P. Gurka, P. Harjulehto and A. Nekvinda, Bessel potential spaces with variable exponent. Math. Inequal. Appl. 10 (2007), 661-676.
- [9] E. Hernandez and G. Weiss, A First Course on Wavelets, CRC Press, Boca Raton, FL, 1996.
- [10] M. Izuki, Wavelets and modular inequalities in variable Lp spaces, Georgian Math. J. 15 (2008), 281-293.
- [11] M. Izuki, The characterizations of weighted Sobolev spaces by wavelets and scaling functions, Taiwanese J. Math. 13 (2009), 467-492.
- [12] S. E. Kelly, M. A. Kon and L. A. Raphael, Local convergence for wavelet expansions, J. Funct. Anal. 126 (1994), 102-138.
- [13] T. S. Kopaliani, Greediness of the wavelet system in Lp(t)(R) spaces. East J. Approx. 14 (2008), 59-67.
- [14] O. Kovacik and J. Rakosnfk, On spaces Lp(x) and Wk,p(x), Czechoslovak Math. J. 41(116) (1991), 592-618.
- [15] Y. Meyer, Wavelets and Operators, Cambridge University Press, Cambridge, 1992.
- [16] N. Miller, Weighted Sobolev spaces and pseudodifferential operators with smooth symbols, Trans. Amer. Math. Soc. 269 (1982), 91-109.
- [17] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
- [18] E. Nakai, N. Tomita and K. Yabuta, Density of the set of all infinitely differentiable functions with compact support in weighted Sobolev spaces, Sci. Math. Jpn. 60(2004), 121-127.
- [19] A. Nekvinda, Hardy-Littlewood maximal operator on Lp(x)(Rn), Math. Inequal. Appl. 7 (2004), 255-265.
- [20] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1971.
- [21] P. Wojtaszczyk, A Mathematical Introduction to Wavelets, Cambridge University Press, Cambridge, 1997.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD7-0033-0012