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1995 | 115 | 2 | 151-181
Tytuł artykułu

Double exponential integrability, Bessel potentials and embedding theorems

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This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.
Twórcy
  • Centre for Mathematical Analysis and its Applications, The University of Sussex, Falmer, Brighton BN1 9QH, England, d.e.edmunds@sussex.ac.uk
autor
  • Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Prague 1, Czech Republic., opic@earn.cvut.cz
Bibliografia
  • [1] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
  • [2] C. Bennett and K. Rudnick, On Lorentz-Zygmund spaces, Dissertationes Math. 175 (1980).
  • [3] C. Bennett and R. Sharpley, Interpolation of Operators, Pure Appl. Math. 129, Academic Press, 1988.
  • [4] H. Brézis and S. Wainger, A note on limiting cases of Sobolev embeddings and convolution inequalities, Comm. Partial Differential Equations 5 (1980), 773-789.
  • [5] D. E. Edmunds, P. Gurka and B. Opic, Double exponential integrability of convolution operators in generalized Lorentz-Zygmund spaces, Indiana Univ. Math. J. (1995), to appear.
  • [6] D. E. Edmunds and M. Krbec, Two limiting cases of Sobolev imbeddings, preprint no. 89, Math. Inst. Czech Acad. Sci., Prague, 1994, 8 pp.
  • [7] W. D. Evans, B. Opic and L. Pick, Interpolation of operators on scales of generalized Lorentz-Zygmund spaces, preprint no. 99, Math. Inst. Czech Acad. Sci., Prague, 1995, 57 pp.
  • [8] N. Fusco, P. L. Lions and C. Sbordone, Some remarks on Sobolev embeddings in borderline cases, preprint no. 25, Università degli Studi di Napoli "Federico II", 1993, 7 pp.
  • [9] A. Kufner, O. John and S. Fučík, Function Spaces, Academia, Prague, 1977.
  • [10] G. Lorentz, On the theory of spaces Λ, Pacific J. Math. 1 (1951), 411-429.
  • [11] F. J. Martín-Reyes and E. T. Sawyer, Weighted inequalities for Riemann-Liouville fractional integrals of order one and greater, Proc. Amer. Math. Soc. 106 (1989) 727-733.
  • [12] R. O'Neil, Convolution operators and L(p,q) spaces, Duke Math. J. 30 (1963), 129-142.
  • [13] E. T. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), 145-158.
  • [14] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.
  • [15] V. D. Stepanov, Weighted inequalities for a class of Volterra convolution operators, J. London Math. Soc. 45 (1992), 232-242.
  • [16] V. D. Stepanov, The weighted Hardy's inequality for non-increasing functions, Trans. Amer. Math. Soc. 338 (1993), 173-186.
  • [17] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
  • [18] N. S. Trudinger, On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473-484.
  • [19] W. P. Ziemer, Weakly Differentiable Functions, Graduate Texts in Math. 120, Springer, Berlin, 1989.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv115i2p151bwm
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