Convergence in nonisotropic regions of harmonic functions in n

Carme Cascante; Joaquin Ortega

Studia Mathematica (1999)

  • Volume: 134, Issue: 3, page 269-298
  • ISSN: 0039-3223

Abstract

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We study the boundedness in L p ( n ) of the projections onto spaces of functions with spectrum contained in horizontal strips. We obtain some results concerning convergence along nonisotropic regions of harmonic extensions of functions in L p ( n ) with spectrum included in these horizontal strips.

How to cite

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Cascante, Carme, and Ortega, Joaquin. "Convergence in nonisotropic regions of harmonic functions in $^n$." Studia Mathematica 134.3 (1999): 269-298. <http://eudml.org/doc/216638>.

@article{Cascante1999,
abstract = {We study the boundedness in $L^p(^n)$ of the projections onto spaces of functions with spectrum contained in horizontal strips. We obtain some results concerning convergence along nonisotropic regions of harmonic extensions of functions in $L^p(^n)$ with spectrum included in these horizontal strips.},
author = {Cascante, Carme, Ortega, Joaquin},
journal = {Studia Mathematica},
keywords = {harmonic and holomorphic functions; tangential convergence; boundary behaviour; admissible approach regions; theorems of Fatou type; bigraded spherical harmonics; Cauchy-Szegő projection; potentials; Sobolev spaces; Riesz-type kernels; complex interpolation; admissible convergence; admissible maximal functions; transverse curves; Hardy-Sobolev spaces; Riesz potentials; almost everywhere convergence},
language = {eng},
number = {3},
pages = {269-298},
title = {Convergence in nonisotropic regions of harmonic functions in $^n$},
url = {http://eudml.org/doc/216638},
volume = {134},
year = {1999},
}

TY - JOUR
AU - Cascante, Carme
AU - Ortega, Joaquin
TI - Convergence in nonisotropic regions of harmonic functions in $^n$
JO - Studia Mathematica
PY - 1999
VL - 134
IS - 3
SP - 269
EP - 298
AB - We study the boundedness in $L^p(^n)$ of the projections onto spaces of functions with spectrum contained in horizontal strips. We obtain some results concerning convergence along nonisotropic regions of harmonic extensions of functions in $L^p(^n)$ with spectrum included in these horizontal strips.
LA - eng
KW - harmonic and holomorphic functions; tangential convergence; boundary behaviour; admissible approach regions; theorems of Fatou type; bigraded spherical harmonics; Cauchy-Szegő projection; potentials; Sobolev spaces; Riesz-type kernels; complex interpolation; admissible convergence; admissible maximal functions; transverse curves; Hardy-Sobolev spaces; Riesz potentials; almost everywhere convergence
UR - http://eudml.org/doc/216638
ER -

References

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