TheLp-integrability of the partial derivatives of A quasiconformal mapping

@article{Gehring1973TheLpintegrabilityOT,
  title={TheLp-integrability of the partial derivatives of A quasiconformal mapping},
  author={F. Gehring},
  journal={Acta Mathematica},
  year={1973},
  volume={130},
  pages={265-277}
}
  • F. Gehring
  • Published 1973
  • Mathematics
  • Acta Mathematica
Jf(x) = lim sup m(f(B(x, r)))/m(B(x, r)), r->0 where B(x, r) denotes the open ^-dimensional ball of radius r about x and m denotes Lebesgue measure in R. We call Lf(x) and Jf(x\ respectively, the maximum stretching and generalized Jacobian for the homeomorphism ƒ at the point x. These functions are nonnegative and measurable in D, and Lebesgue's theorem implies that Jf is locally LMntegrable there. Suppose in addition that ƒ is X-quasiconformal in D. Then Lf ^ KJf a.e. in D, and thus Lf is… Expand

References

SHOWING 1-10 OF 14 REFERENCES
Quasiconformal mappings in space
On the existence of certain singular integrals
Quasi-conformal mappings inn-space and the rigidity of hyperbolic space forms
Symmetrization of rings in space
Homeomorfisme cvasiconforme n-dimensionale
On functions of bounded mean oscillation
RINGS AND QUASICONFORMAL MAPPINGS IN SPACE.
  • F. Gehring
  • Medicine, Mathematics
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1961
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