Anisotropic Two-Microlocal Spaces and Regularity

Mourad Ben Slimane
2014 Journal of Function Spaces  
We defineD-u-anisotropic two-microlocal spaces by decay conditions on anisotropic wavelet coefficients on anyD-u-anisotropic wavelet basis ofL2(Rd). We prove that these spaces allow the characterizing of pointwise anisotropic Hölder regularity. We also prove an anisotropic wavelet criterion for anisotropic uniform regularity. We finally prove that both this criterion and anisotropicD-u-two-microlocal spaces are independent of the chosen anisotropicD-u-orthonormal wavelet basis.
doi:10.1155/2014/505796 fatcat:s3wmp4agifge5ciaklqmnrio5y