The wavelet type systems
We consider biorthogonal systems of functions on the interval [0,1] or 𝕋 which have the same dyadic scaled estimates as wavelets. We present properties and examples of these systems.
We consider biorthogonal systems of functions on the interval [0,1] or 𝕋 which have the same dyadic scaled estimates as wavelets. We present properties and examples of these systems.
We study smoothness spaces generated by maximal functions related to the local approximation errors of integral operators. It turns out that in certain cases these smoothness classes coincide with the spaces , 0 < p≤∞, introduced by DeVore and Sharpley [DS] by means of the so-called sharp maximal functions of Calderón and Scott. As an application we characterize the spaces in terms of the coefficients of wavelet decompositions.
We give a weighted version of the Sobolev-Lieb-Thirring inequality for suborthonormal functions. In the proof of our result we use phi-transform of Frazier-Jawerth.