Spaces Of Quaternion-valued Functions Research Articles

Q_K-Type Spaces of Quaternion-Valued Functions

In this paper we develop the necessary tools to generalize the Q_K-type function classes to the case of the monogenic functions defined in the unit ball of R^3, some important basic properties of these functions are also considered. Further, we show some relations between Q_K(p,q) and α-Bloch spaces of quaternion-valued functions.

Quaternionic Stockwell transform

ABSTRACTIn this article, we extend the Stockwell transform to the space of all square integrable quaternion-valued functions on the real line, using the convolution of quaternion-valued functions. We prove that the extended Stockwel transform satisfies the Parseval's formula, inversion formula, and uncertainty principle. We also characterize the range of the Stockwell transform on and prove a convolution theorem for the extended Stockwell transform. Applying the convolution theorem, we extend the transform to a suitable Boehmian space of quaternion-valued functions.

Quaternionic $$F (p,q,s)$$ F ( p , q , s ) Function Spaces

In this paper we develop the necessary tools to generalize the function spaces \(F(p,q,s)\) and \(F_0(p,q,s)\) introduced by Zhao in (Zhao, Ann Acad Sci Fenn Math Diss No 105, 1996) to the case of the monogenic functions defined in the unit ball of \(\mathbb {R}^3\). Obtaining at the same time the generalization of \({\mathcal {Q}}_p\) monogenic spaces presented in (Gurlebeck et al., On \(\mathbb {Q}_{p}-\)spaces of quaternion-valued functions, 1999) and \(B^{q,p}\) monogenic spaces in (El-Sayed Ahmed et al., Complex Var Elliptic Equ 51(2):119–136, 2006).

Lacunary series in quaternion Bp,q spaces

The main theme of this article is to obtain characterizations of B p,q -functions by the coefficients of certain lacunary series expansions in quaternionic sense. Moreover, we consider a scale of weighted spaces of quaternion-valued functions of three real variables. This scale generalizes the idea of Besov space in the complex function theory. Finally, we prove that the inclusions of spaces from the scale are strict inclusions.

On Weighted α-Besov Spaces and α-Bloch Spaces of Quaternion-Valued Functions

In this paper, we give the definitions of weighted α-Besov-type spaces and α-Bloch spaces of quaternion-valued functions, then we obtain characterizations of these quaternion α-Bloch spaces by quaternion α-Besov-type spaces. Relations between Q p norms and weighted α-Besov norms are also considered. The role of ρℬα sequences in securing non-Bloch functions is highlighted in quaternion sense.