An estimate of the Hopf degree of fractional Sobolev mappings (1904.12549v1)

Published 29 Apr 2019 in math.AP, math.AT, and math.FA

Abstract: We estimate the Hopf degree for smooth maps $f$ from $\mathbb{S}^{4n-1}$ to $\mathbb{S}^{2n}$ in the fractional Sobolev space. Namely we show that for $s \in [1 - \frac{1}{4n}, 1]$ [ \left |{\rm deg}H(f)\right | \lesssim [f]{W^{{s,\frac{4n-1}{s}}}^{{\frac{4n}{s}}.}} ] Our argument is based on the Whitehead integral formula and commutator estimates for Jacobian-type expressions.

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