Asymmetric Hölder Spaces of Sign Sensitive Weighted Integrable Functions - Jiménez-Pozo, Miguel A.; Hernández-Morales, José M. (Communications in Mathematics and Applications, 2012)
We consider the space $L( u,v) $ of $2π$-periodic real-valued functions which are integrable with respect to a sign sensitive weight ${(u,v)}$. With some necessary hypothesis for this weight, $L( u,v) $ is an asymmetric Banach space. After defining a convenient modulus of smoothness we introduce the corresponding space $Lip_{α}(u,v) $ and its subspace $lip_{α }( u,v) $ of Hölder (or Lipschitz) functions associated to this modulus. We prove these spaces are asymmetric Banach spaces too and use the result to study approximation problems.