F. Soltani

We introduce generalized Lipschitz classes $\mbox{Lip}^M(\eta)$ and $\mbox{lip}^M(\eta)$ of functions associated with the canonical Sturm-Liouville operator \[L^M:=\frac{\mbox{d}^2}{\mbox{d}x^2}+\left(\frac{A'(x)}{A(x)}-2i\frac{a}{b}x\right)\frac{\mbox{d}}{\mbox{d}x} -\left(\frac{a^2}{b^2}x^2+i\frac{a}{b}x\frac{A'(x)}{A(x)}+i\frac{a}{b}\right),\] where $A$ is a nonnegative function satisfying certain conditions; and we prove two versions of Boas-type theorems for the canonical Sturm-Liouville transform $\mathscr{F}^M$. An application to the canonical Sturm-Liouville multipliers is given. Boas-type results for the canonical Fourier-Bessel transform and the canonical Fourier-Jacobi transform are special cases of this work.