Besov‐type spaces associated with Lebedev‐Skalskaya wavelet transform.

In the current study, we define Besov‐type spaces related to the Lebedev‐Skalskaya (LS‐) transform. We obtain Parseval's relation for continuous LS‐wavelet transform in L2(ℝ+;dx)$$ {L}^2\left({\mathrm{\mathbb{R}}}^{+}; dx\right) $$ space, and then using it, we extend the notion of continuous LS‐wavelet transform on Lp(ℝ+;dx)$$ {L}^p\left({\mathrm{\mathbb{R}}}^{+}; dx\right) $$ space and, in the end, derive continuity of LS‐wavelet transform on Besov‐type spaces and characterize the Besov LS‐space using LS‐wavelet coefficients. [ABSTRACT FROM AUTHOR]