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.