Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 


Lattice property of $ p$-admissible weights

Authors: Tero Kilpeläinen, Pekka Koskela and Hiroaki Masaoka
Journal: Proc. Amer. Math. Soc. 143 (2015), 2427-2437
MSC (2010): Primary 46E35
Published electronically: February 3, 2015
MathSciNet review: 3326025
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that, for large $ p$'s, the maximum of two $ p$-admissible weights remains $ p$-admissible in the terminology of nonlinear potential theory. We also give examples showing that in general, the minimum may fail to remain $ p$-admissible.

References [Enhancements On Off] (What's this?)

  • [1] Anders Björn and Jana Björn, Nonlinear potential theory on metric spaces, EMS Tracts in Mathematics, vol. 17, European Mathematical Society (EMS), Zürich, 2011. MR 2867756
  • [2] Jana Björn, Stephen Buckley, and Stephen Keith, Admissible measures in one dimension, Proc. Amer. Math. Soc. 134 (2006), no. 3, 703-705 (electronic). MR 2180887 (2006k:26021),
  • [3] Seng-Kee Chua and Richard L. Wheeden, Sharp conditions for weighted 1-dimensional Poincaré inequalities, Indiana Univ. Math. J. 49 (2000), no. 1, 143-175. MR 1777034 (2001h:26021),
  • [4] Eugene B. Fabes, Carlos E. Kenig, and Raul P. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982), no. 1, 77-116. MR 643158 (84i:35070),
  • [5] José García-Cuerva and José L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Mathematics Studies, vol. 116, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 104. MR 807149 (87d:42023)
  • [6] Piotr Hajłasz and Pekka Koskela, Sobolev met Poincaré, Mem. Amer. Math. Soc. 145 (2000), no. 688, x+101. MR 1683160 (2000j:46063),
  • [7] Juha Heinonen, Lectures on analysis on metric spaces, Universitext, Springer-Verlag, New York, 2001. MR 1800917 (2002c:30028)
  • [8] Juha Heinonen, Tero Kilpeläinen, and Olli Martio, Nonlinear potential theory of degenerate elliptic equations, Dover Publications Inc., Mineola, NY, 2006. Unabridged republication of the 1993 original. MR 2305115 (2008g:31019)
  • [9] Stephen Keith and Xiao Zhong, The Poincaré inequality is an open ended condition, Ann. of Math. (2) 167 (2008), no. 2, 575-599. MR 2415381 (2009e:46028),
  • [10] V. G. Mazja, On the theory of the higher-dimensional Schrödinger operator, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1145-1172 (Russian). MR 0174879 (30 #5070)
  • [11] Pekka Tukia, Hausdorff dimension and quasisymmetric mappings, Math. Scand. 65 (1989), no. 1, 152-160. MR 1051832 (92b:30026)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46E35

Retrieve articles in all journals with MSC (2010): 46E35

Additional Information

Tero Kilpeläinen
Affiliation: Department of Mathematics and Statistics, P.O. Box 35, FI-40014 University of Jyväskylä, Finland

Pekka Koskela
Affiliation: Department of Mathematics and Statistics, P.O. Box 35, FI-40014 University of Jyväskylä, Finland

Hiroaki Masaoka
Affiliation: Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Kamigamo, Motoyama, Kita-ku, Kyoto 603-8555, Japan

Received by editor(s): December 21, 2012
Received by editor(s) in revised form: November 16, 2013
Published electronically: February 3, 2015
Communicated by: Jeremy T. Tyson
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society