The Abel summation of the inverse Fourier transform of the homogeneous functions in $R^n$

As is well known, the most commonly used functions on a line are powerful functions. A multidimensional analogue of power functions is homogeneous functions, which look like $\theta (\tau )|t|^\alpha$ and have an arbitrary function on a unit sphere additionally to the parameter $\alpha$. The inverse Fourier transform for these functions results in restrictions for an order of $\alpha$. One approach to improve convergence is Abel summation. Abel summation formulas for inverse Fourier transform of homogeneous functions have been derived in the article, which look like $\theta (\tau )|t|^\alpha$, $\tau \in S^{n-1}=\{t \in \mathbb{R}^n: |t|=1\}$ for various function spaces on a unit sphere.