Construction of wavelets in $W_2^m(\mathbb R)$ and their approximative properties in different metrics

Wavelet bases in the Sobolev space $W_2^m(\mathbb R)$ on the axis $\mathbb R=(-\infty,\infty)$ orthogonal with respect to any given inner product generating one of equivalent norms in $W_2^m(\mathbb R)$ are constructed. The rate of convergence of series in these bases for smooth functions from $L_q(\mathbb R)$ ($2\le q\le\infty$) is investigated.