On the duality of variable Triebel–Lizorkin spaces

• Autores: Douadi Drihem
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 2, 2020, págs. 263-278
• Idioma: inglés
• DOI: 10.1007/s13348-019-00258-1
• Texto completo no disponible (Saber más ...)
• Resumen

  • The aim of this paper is to prove the duality of Triebel–Lizorkin spaces F_{1,q\left( \cdot \right) }^{\alpha \left( \cdot \right) }. First, we prove the duality of associated sequence spaces. The result follows from the so-called \varphi-transform characterization in the sense of Frazier and Jawerth.

• Referencias bibliográficas
  • Almeida, A., Hästö, P.: Besov spaces with variable smoothness and integrability. J. Funct. Anal. 258, 1628–1655 (2010)
  • Besov, O.: On spaces of functions of variable smoothness defined by pseudodifferential operators. Tr. Mat. Inst. Steklova 227 (1999), Issled....
  • Besov, O.: Equivalent normings of spaces of functions of variable smoothness. (Russian) Tr. Mat. Inst. Steklova 243 (2003), Funkts. Prostran.,...
  • Besov, O.: Interpolation, embedding, and extension of spaces of functions of variable smoothness. (Russian) Tr. Mat. Inst. Steklova 248 (2005),...
  • Cruz-Uribe, D., Fiorenza, A.: Variable Lebesgue Spaces: Foundations and Harmonic Analysis. Applied and Numerical Harmonic Analysis. Birkhauser,...
  • Chen, Y., Levine, S., Rao, R.: Variable exponent, linear growth functionals in image restoration. SIAM J. Appl. Math. 66(4), 1383–1406 (2006)
  • Diening, L., Hästö, P., Roudenko, S.: Function spaces of variable smoothness and integrability. J. Funct. Anal. 256(6), 1731–1768 (2009)
  • Diening, L., Harjulehto, P., Hästö, P., Růž ička, M.: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics, vol....
  • Drihem, D.: Characterizations of Besov-type and Triebel–Lizorkin-type spaces by differences. J. Funct. Spaces Appl. 2012, Article ID 328908,...
  • Drihem, D.: Atomic decomposition of Besov-type and Triebel–Lizorkin-type spaces. Sci. China Math. 56(5), 1073–1086 (2013)
  • Drihem, D.: Some properties of variable Besov-type spaces. Funct. Approx. Comment. Math. 52(2), 193–221 (2015)
  • Drihem, D.: Some characterizations of variable Besov-type spaces. Ann. Funct. Anal. 6(4), 255–288 (2015)
  • Diening, L., Harjulehto, P., Hästö, P., Mizuta, Y., Shimomura, T.: Maximal functions in variable exponent spaces: limiting cases of the exponent....
  • Frazier, M., Jawerth, B.: A discrete transform and decomposition of distribution spaces. J. Funct. Anal. 93(1), 34–170 (1990)
  • Izuki, M., Noi, T.: Duality of Besov, Triebel–Lizorkin and Herz spaces with variable exponents. Rend. Circ. Mat. Palermo. 63, 221–245 (2014)
  • Kempka, H., Vybíral, J.: A note on the spaces of variable integrability and summability of Almeida and Hästö. Proc. Am. Math. Soc. 141(9),...
  • Kempka, H., Vybíral, J.: Spaces of variable smoothness and integrability: characterizations by local means and ball means of differences....
  • Leopold, H.-G.: On Besov spaces of variable order of differentiation. Z. Anal. Anwen-dungen 8(1), 69–82 (1989)
  • Leopold, H.-G.: Interpolation of Besov spaces of variable order of differentiation. Arch. Math. (Basel) 53(2), 178–187 (1989)
  • Leopold, H.-G.: On function spaces of variable order of differentiation. Forum Math. 3, 633–644 (1991)
  • Leopold, H.-G.: Embedding of function spaces of variable order of differentiation in function spaces of variable order of integration. Czechoslovak...
  • Leopold, H.-G., Schrohe, E.: Trace theorems for Sobolev spaces of variable order of differentiation. Math. Nachr. 179, 223–245 (1996)
  • Noi, T.: Duality of variable exponent Triebel-Lizorkin and Besov spaces. J. Funct. Spaces Appl., Art. ID 361807, 19 pp (2012)
  • Runst, T., Sickel, W.: Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations. de Gruyter Series...
  • Růžička, M.: Electrorheological Fluids: Modeling and Mathematical Theory. Lecture Notes in Mathematics, vol. 1748. Springer, Berlin (2000)
  • Triebel, H.: Spaces of distributions of Besov type on Euclidean $n$-space. Duality, interpolation. Ark. Mat. 11, 13–64 (1973)
  • Triebel, H.: Theory of Function Spaces. Birkhäuser Verlag, Basel (1983)
  • Triebel, H.: Theory of Function Spaces II. Birkhä user Verlag, Basel (1992)
  • Tyulenev, A.I.: Some new function spaces of variable smoothness. Sb. Math. 206(6), 849–891 (2015)
  • Tyulenev, A.I.: On various approaches to Besov-type spaces of variable smoothness. J. Math. Anal. Appl. 451, 371–392 (2017)
  • Vybíral, J.: Sobolev and Jawerth embeddings for spaces with variable smoothness and integrability. Ann. Acad. Sci. Fenn. Math. 34(2), 529–544...
  • Yang, D., Zhuo, C., Yuan, W.: Triebel–Lizorkin-type spaces with variable exponents. Banach J. Math. Anal. 9(4), 146–202 (2015)
  • Yang, D., Zhuo, C., Yuan, W.: Besov-type spaces with variable smoothness and integrability. J. Funct. Anal. 269(6), 1840–1898 (2015)
  • Yuan, W., Sickel, W., Yang, D.: Morrey and Campanato Meet Besov. Lizorkin and Triebel Lecture Notes in Mathematics, vol. 2005. Springer, Berlin...
  • Xu, J.: Variable Besov and Triebel–Lizorkin spaces. Ann. Acad. Sci. Fenn. Math. 33, 511–522 (2008)
  • Xu, J.: An atomic decomposition of variable Besov and Triebel–Lizorkin spaces. Armen. J. Math. 2(1), 1–12 (2009)