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Averaging operators over nondegenerate quadratic surfaces in finite fields

  • Doowon Koh EMAIL logo
Published/Copyright: March 29, 2013
Forum Mathematicum
From the journal Forum Mathematicum Volume 27 Issue 2

Abstract

We study mapping properties of the averaging operator related to the variety V={x∈𝔽qd:Q(x)=0}, where Q(x) is a nondegenerate quadratic polynomial over a finite field 𝔽q with q elements. This paper is devoted to eliminating the logarithmic bound proved by Koh and Shen (to appear in Proc. Edinb. Math. Soc.). As a consequence, we settle down the averaging problems over the quadratic surfaces V in the case when the dimensions d ≥ 4 are even and V contains a d/2-dimensional subspace.

Keywords: Averaging operator; finite fields
MSC: 43A32; 43A15; 11T99

Funding source: Chungbuk National University

Funding source: National Research Foundation of Korea (NRF)

Award Identifier / Grant number: 2012010487

The author would like to thank the referee for his/her valuable comments for developing the final version of this paper.

Received: 2012-9-10
Revised: 2012-12-19
Published Online: 2013-3-29
Published in Print: 2015-3-1

© 2015 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Near abelian profinite groups
  3. On Calabi–Yau threefolds associated to a web of quadrics
  4. On the partial fraction decomposition of the restricted partition generating function
  5. Projectively flat Finsler manifolds with infinite dimensional holonomy
  6. Weighted version of Carleson measure and multilinear Fourier multiplier
  7. Injective objects and retracts of Fraïssé limits
  8. On hypersurfaces containing projective varieties
  9. Additive reducts of algebraically closed valued fields
  10. On the subconvexity problem for GL(3) × GL(2) L-functions
  11. An algebraic property of Hecke operators and two indefinite theta series
  12. Sum formula of multiple Hurwitz-zeta values
  13. Classification of homogeneous holomorphic hermitian principal bundles over G/K
  14. Integrality properties of the CM-values of certain weak Maass forms
  15. Heat kernel for fractional diffusion operators with perturbations
  16. New class of multiple weights and new weighted inequalities for multilinear operators
  17. Balanced Hermitian geometry on 6-dimensional nilmanifolds
  18. Extensions of tame algebras and finite group schemes of domestic representation type
  19. Weighted estimates for multilinear Fourier multipliers
  20. Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
  21. From ring epimorphisms to universal localisations
  22. Brauer algebras of type B
  23. Existence problems for the p-Laplacian
  24. Averaging operators over nondegenerate quadratic surfaces in finite fields
  25. Lawson homology for abelian varieties
https://doi.org/10.1515/forum-2012-0135
Keywords for this article
Averaging operator; finite fields

Articles in the same Issue

  1. Frontmatter
  2. Near abelian profinite groups
  3. On Calabi–Yau threefolds associated to a web of quadrics
  4. On the partial fraction decomposition of the restricted partition generating function
  5. Projectively flat Finsler manifolds with infinite dimensional holonomy
  6. Weighted version of Carleson measure and multilinear Fourier multiplier
  7. Injective objects and retracts of Fraïssé limits
  8. On hypersurfaces containing projective varieties
  9. Additive reducts of algebraically closed valued fields
  10. On the subconvexity problem for GL(3) × GL(2) L-functions
  11. An algebraic property of Hecke operators and two indefinite theta series
  12. Sum formula of multiple Hurwitz-zeta values
  13. Classification of homogeneous holomorphic hermitian principal bundles over G/K
  14. Integrality properties of the CM-values of certain weak Maass forms
  15. Heat kernel for fractional diffusion operators with perturbations
  16. New class of multiple weights and new weighted inequalities for multilinear operators
  17. Balanced Hermitian geometry on 6-dimensional nilmanifolds
  18. Extensions of tame algebras and finite group schemes of domestic representation type
  19. Weighted estimates for multilinear Fourier multipliers
  20. Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
  21. From ring epimorphisms to universal localisations
  22. Brauer algebras of type B
  23. Existence problems for the p-Laplacian
  24. Averaging operators over nondegenerate quadratic surfaces in finite fields
  25. Lawson homology for abelian varieties
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