On the differentiability of Lipschitz-Besov functions

Dorronsoro, José R.

doi:10.1090/S0002-9947-1987-0896019-5

On the differentiability of Lipschitz-Besov functions
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Trans. Amer. Math. Soc. 303 (1987), 229-240 Request permission

Abstract:

${L^r}$ and ordinary differentiability is proved for functions in the Lipschitz-Besov spaces $B_a^{p,q},\;1 \leqslant p < \infty ,\;1 \leqslant q \leqslant \infty ,\;a > 0$, using certain maximal operators measuring smoothness. These techniques allow also the study of lacunary directional differentiability and of tangential convergence of Poisson integrals.

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