Dirac Operators, Multipliers and H[superscript P] Spaces of Monogenic Functions

We have done a few things under Clifford algebra settings. Firstly, one Caccioppoli type estimate is derived for solutions of $A$-Dirac equations in the form $DA(x,Du) = 0$, where $D$ is the Dirac operator. This kind of $A$-Dirac equations are generalizations of elliptic equations of $A$-harmonic type, i.e. div$A(x,\nabla u)=0.$ Secondly, the multiplier theory from Fourier analysis is generalized to Clifford analysis. After the multipliers of operators $\mathcal{D}$, $T$ and $ \Pi$ are identified, some related properties will be very easy to achieve, including two integral representation theorems, also the iterations of operators $\mathcal{D}$ and $\Delta$ are also discussed. Thirdly, one Carleson measure theorem is achieved for monogenic Hardy spaces on the unit ball in $R^{n+1}$, as well as one Clifford Riesz representation theorem. Furthermore, one bounded theorem about certain inhomogeneous Dirac equations is established with the help of spherical monogenic functions theory.