Alternative characterisations of Lorentz-Karamata spaces

David Eric Edmunds; Bohumír Opic

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 2, page 517-540
  • ISSN: 0011-4642

Abstract

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We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.

How to cite

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Edmunds, David Eric, and Opic, Bohumír. "Alternative characterisations of Lorentz-Karamata spaces." Czechoslovak Mathematical Journal 58.2 (2008): 517-540. <http://eudml.org/doc/31227>.

@article{Edmunds2008,
abstract = {We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.},
author = {Edmunds, David Eric, Opic, Bohumír},
journal = {Czechoslovak Mathematical Journal},
keywords = {Lorentz-Karamata spaces; equivalent quasi-norms; weighted norm inequalities; fractional maximal operators; Riesz potentials; equivalent quasi-norms; weighted norm inequalities; fractional maximal operators; Riesz potentials},
language = {eng},
number = {2},
pages = {517-540},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Alternative characterisations of Lorentz-Karamata spaces},
url = {http://eudml.org/doc/31227},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Edmunds, David Eric
AU - Opic, Bohumír
TI - Alternative characterisations of Lorentz-Karamata spaces
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 517
EP - 540
AB - We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.
LA - eng
KW - Lorentz-Karamata spaces; equivalent quasi-norms; weighted norm inequalities; fractional maximal operators; Riesz potentials; equivalent quasi-norms; weighted norm inequalities; fractional maximal operators; Riesz potentials
UR - http://eudml.org/doc/31227
ER -

References

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  15. On equivalent quasi-norms on Lorentz spaces, In Function Spaces, Differential Operators and Nonlinear Analysis. The Hans Triebel Aniversary Volume, D. Haroske, T. Runst, H.-J. Schmeisser (eds.), Birkhäuser Verlag, Basel/Switzerland, 2003, pp. 415–426. (2003) Zbl1036.46022MR1984189
  16. 10.1017/S0305004102006321, Math. Proc. Camb. Phil. Soc. 134 (2003), 347–384. (2003) MR1972143DOI10.1017/S0305004102006321

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