# Double exponential integrability, Bessel potentials and embedding theorems

David Edmunds; Petr Gurka; Bohumír Opic

Studia Mathematica (1995)

- Volume: 115, Issue: 2, page 151-181
- ISSN: 0039-3223

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topEdmunds, David, Gurka, Petr, and Opic, Bohumír. "Double exponential integrability, Bessel potentials and embedding theorems." Studia Mathematica 115.2 (1995): 151-181. <http://eudml.org/doc/216205>.

@article{Edmunds1995,

abstract = {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.},

author = {Edmunds, David, Gurka, Petr, Opic, Bohumír},

journal = {Studia Mathematica},

keywords = {Bessel potential; Riesz potential, generalized Lorentz-Zygmund spaces; exponential integrability; Hardy inequality; Orlicz spaces; Bessel potential spaces; double exponential integrability of the Bessel potential; Lorentz-Zygmund spaces},

language = {eng},

number = {2},

pages = {151-181},

title = {Double exponential integrability, Bessel potentials and embedding theorems},

url = {http://eudml.org/doc/216205},

volume = {115},

year = {1995},

}

TY - JOUR

AU - Edmunds, David

AU - Gurka, Petr

AU - Opic, Bohumír

TI - Double exponential integrability, Bessel potentials and embedding theorems

JO - Studia Mathematica

PY - 1995

VL - 115

IS - 2

SP - 151

EP - 181

AB - 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.

LA - eng

KW - Bessel potential; Riesz potential, generalized Lorentz-Zygmund spaces; exponential integrability; Hardy inequality; Orlicz spaces; Bessel potential spaces; double exponential integrability of the Bessel potential; Lorentz-Zygmund spaces

UR - http://eudml.org/doc/216205

ER -

## References

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- [9] A. Kufner, O. John and S. Fučík, Function Spaces, Academia, Prague, 1977.
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- [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. Zbl0705.42014
- [14] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0207.13501
- [15] V. D. Stepanov, Weighted inequalities for a class of Volterra convolution operators, J. London Math. Soc. 45 (1992), 232-242. Zbl0703.42011
- [16] V. D. Stepanov, The weighted Hardy's inequality for non-increasing functions, Trans. Amer. Math. Soc. 338 (1993), 173-186. Zbl0786.26015
- [17] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. Zbl0387.46033
- [18] N. S. Trudinger, On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473-484. Zbl0163.36402
- [19] W. P. Ziemer, Weakly Differentiable Functions, Graduate Texts in Math. 120, Springer, Berlin, 1989.

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