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In this paper we introduce the one-sided sharp functions defined by \[ f_ +^ \# (x) = \sup_{h > 0} {1 \over h} \int^{x + h}_ x \left( f(y) - {1 \over h} \int^{x + 2h}_{x + h} f \right)^ + dy \] and \[ f_ -^ \# (x) = \sup_{h > 0} {1 \over h} \int^ x_{x - h} \left( f(y) - {1 \over h} \int^{x - h}_{x-2h} f \right)^ + dy \] where \(z^ + = \max (z,0)\).
Martín-Reyes, F. J., de la Torre, A.
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Let \(A\in B(\ell_2)\) having the representation as a matrix \(A=(a(i,j))_{i,j=1}^\infty\).
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BMO and Injectivity of Space Quasiregular Mappings
Mathematische Nachrichten, 1999AbstractIt is shown that if the dilatation tensor G f of a space quasi regular mapping f belongs to the space VMO (vanishing mean oscillation), then f is a local homeomorphism. The same is true If the BMO‐norm of G f is small or if Gf is only close to the VMO space in the BMO‐norm.
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