Anisotropic two-microlocal spaces and regularity (Q403247)

Summary: We define \(D\)-\(\mathbf u\)-anisotropic two-microlocal spaces by decay conditions on anisotropic wavelet coefficients on any \(D\)-\(\mathbf u\)-anisotropic wavelet basis of \(L^2(\mathbb R^d)\). 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 anisotropic \(D\)-\(\mathbf u\)-two-microlocal spaces are independent of the chosen anisotropic \(D\)-\(\mathbf u\)-orthonormal wavelet basis.