On the Choquet integrals associated to Bessel capacities

Keng Hao Ooi

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 2, page 433-447
  • ISSN: 0011-4642

Abstract

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We characterize the Choquet integrals associated to Bessel capacities in terms of the preduals of the Sobolev multiplier spaces. We make use of the boundedness of local Hardy-Littlewood maximal function on the preduals of the Sobolev multiplier spaces and the minimax theorem as the main tools for the characterizations.

How to cite

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Ooi, Keng Hao. "On the Choquet integrals associated to Bessel capacities." Czechoslovak Mathematical Journal 72.2 (2022): 433-447. <http://eudml.org/doc/298299>.

@article{Ooi2022,
abstract = {We characterize the Choquet integrals associated to Bessel capacities in terms of the preduals of the Sobolev multiplier spaces. We make use of the boundedness of local Hardy-Littlewood maximal function on the preduals of the Sobolev multiplier spaces and the minimax theorem as the main tools for the characterizations.},
author = {Ooi, Keng Hao},
journal = {Czechoslovak Mathematical Journal},
keywords = {Choquet integral; Bessel capacity; Hardy-Littlewood maximal function},
language = {eng},
number = {2},
pages = {433-447},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Choquet integrals associated to Bessel capacities},
url = {http://eudml.org/doc/298299},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Ooi, Keng Hao
TI - On the Choquet integrals associated to Bessel capacities
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 2
SP - 433
EP - 447
AB - We characterize the Choquet integrals associated to Bessel capacities in terms of the preduals of the Sobolev multiplier spaces. We make use of the boundedness of local Hardy-Littlewood maximal function on the preduals of the Sobolev multiplier spaces and the minimax theorem as the main tools for the characterizations.
LA - eng
KW - Choquet integral; Bessel capacity; Hardy-Littlewood maximal function
UR - http://eudml.org/doc/298299
ER -

References

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  4. Grigor'yan, A., Verbitsky, I., 10.2422/2036-2145.201802_011, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 20 (2020), 721-750. (2020) Zbl07328846MR4105916DOI10.2422/2036-2145.201802_011
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  6. Maz'ya, V. G., 10.1007/978-3-642-15564-2, Grundlehren der Mathematischen Wissenschaften 342. Springer, Berlin (2011). (2011) Zbl1217.46002MR2777530DOI10.1007/978-3-642-15564-2
  7. Maz'ya, V. G., Shaposhnikova, T. O., 10.1007/978-3-540-69492-2, Grundlehren der Mathematischen Wissenschaften 337. Springer, Berlin (2009). (2009) Zbl1157.46001MR2457601DOI10.1007/978-3-540-69492-2
  8. Maz'ya, V. G., Verbitsky, I. E., 10.1007/BF02559606, Ark. Mat. 33 (1995), 81-115. (1995) Zbl0834.31006MR1340271DOI10.1007/BF02559606
  9. Ooi, K. H., Phuc, N. C., Characterizations of predual spaces to a class of Sobolev multiplier type spaces, Available at https://arxiv.org/abs/2005.04349 (2020), 46 pages. (2020) MR4360359
  10. Ooi, K. H., Phuc, N. C., On a capacitary strong type inequality and related capacitary estimates, Available at https://arxiv.org/abs/2009.09291v1 (2020), 12 pages. (2020) MR4404777

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