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Linked References

1. K. Maurin, Analysis. Part II, D. Reidel, Dordrecht, The Netherlands, PWN-Polish Scientific, Warsaw, Poland, 1980. View at Zentralblatt MATH · View at MathSciNet
2. A. Cialdea, “On the theory of self-conjugate differential forms,” Atti del Seminario Matematico e Fisico dell'Università di Modena, vol. 46, 595 pages, 1998. View at Zentralblatt MATH · View at MathSciNet
3. J. Bory-Reyes and R. Delanghe, “On the structure of solutions of the Moisil-Théodoresco system in Euclidean space,” to appear in Advances in Applied Clifford Algebras.
4. J. Bory-Reyes and R. Delanghe, “On the solutions of the Moisil-Théodoresco system,” to appear in Mathematical Methods in the Applied Sciences. View at Publisher · View at Google Scholar
5. A. Cialdea, “The brothers Riesz theorem for conjugate differential forms in ${ℝ}^n$,” Applicable Analysis, vol. 65, no. 1-2, 69 pages, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
6. R. Dáger and A. Presa, “Duality of the space of germs of harmonic vector fields on a compact,” Comptes Rendus Mathématique. Académie des Sciences. Paris, vol. 343, no. 1, 19 pages, 2006. View at Zentralblatt MATH · View at MathSciNet
7. R. Dáger and A. Presa, “On duality of the space of harmonic vector fields,” arXiv:math.FA/0610924v1, 30 October, 2006.
8. S. Ding, “Some examples of conjugate $p$-harmonic differential forms,” Journal of Mathematical Analysis and Applications, vol. 227, no. 1, 251 pages, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
9. B. Gustafsson and D. Khavinson, “On annihilators of harmonic vector fields,” Rossiĭskaya Akademiya Nauk. Sankt-Peterburgskoe Otdelenie. Matematicheskiĭ Institut im. V. A. Steklova. Zapiski Nauchnykh Seminarov (POMI), vol. 232, 90 pages, 1996, English translation in Journal of Mathematical Sciences, vol. 92, no.1, 3600–3612, 1998, Russian. View at Zentralblatt MATH · View at MathSciNet
10. E. Malinnikova, “Measures orthogonal to the gradients of harmonic functions,” in Complex Analysis and Dynamical Systems, vol. 364 of Contemporary Mathematics, p. 181, American Mathematical Society, Providence, RI, USA, 2004. View at Zentralblatt MATH · View at MathSciNet
11. R. Delanghe and F. Sommen, “On the structure of harmonic multi-vector functions,” Advances in Applied Clifford Algebras, vol. 17, no. 3, 395 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
12. Gr. Moisil and N. Théodoresco, “Functions holomorphes dans l'espace,” Mathematica Cluj, vol. 5, 142 pages, 1931.
13. R. Delanghe, F. Sommen, and V. Souček, Clifford Algebra and Spinor-Valued Functions, vol. 53 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992. View at Zentralblatt MATH · View at MathSciNet
14. J. E. Gilbert and M. A. M. Murray, Clifford Algebras and Dirac Operators in Harmonic Analysis, vol. 26 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1991. View at Zentralblatt MATH · View at MathSciNet
15. K. Gürlebeck, K. Habetha, and W. Sprößig, Funktionentheorie in der Ebene und im Raum, Grundstudium Mathematik, Birkhäuser, Basel, Switzerland, 2006. View at Zentralblatt MATH · View at MathSciNet
16. F. Brackx, R. Delanghe, and F. Sommen, “On conjugate harmonic functions in Euclidean space,” Mathematical Methods in the Applied Sciences, vol. 25, no. 16–18, 1553 pages, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
17. F. Brackx, R. Delanghe, and F. Sommen, “Differential forms and/or multi-vector functions,” Cubo, vol. 7, no. 2, 139 pages, 2005. View at Zentralblatt MATH · View at MathSciNet
18. D. Eelbode and F. Sommen, “Differential forms in Clifford analysis,” in Methods of Complex and Clifford Analysis, p. 41, SAS International Publications, Delhi, India, 2004. View at Zentralblatt MATH · View at MathSciNet
19. F. Trèves, Linear Partial Differential Equations with Constant Coefficients: Existence, Approximation and Regularity of Solutions, vol. 6 of Mathematics and Its Applications, Gordon and Breach, New York, NY, USA, 1966. View at Zentralblatt MATH · View at MathSciNet
20. R. Fueter, “Die Funktionentheorie der Differentialgleichungen $\Delta u=0$ und $\Delta \Delta u=0$ mit vier reellen Variablen,” Commentarii Mathematici Helvetici, vol. 7, no. 1, 307 pages, 1934. View at Publisher · View at Google Scholar · View at MathSciNet
21. A. Sudbery, “Quaternionic analysis,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 85, no. 2, 199 pages, 1979. View at Zentralblatt MATH · View at MathSciNet
22. N. I. Muskhelishvili, Singular Integral Equations, Noordhoff, Leyden, The Netherlands, 1977. View at MathSciNet
23. H. Federer, Geometric Measure Theory, vol. 153 of Die Grundlehren der Mathematischen Wissenschaften, Band, Springer, New York, NY, USA, 1969. View at MathSciNet
24. P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, vol. 44 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1995. View at Zentralblatt MATH · View at MathSciNet
25. G. David and S. Semmes, Analysis of and on Uniformly Rectifiable Sets, vol. 38 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1993. View at Zentralblatt MATH · View at MathSciNet
26. R. Abreu-Blaya and J. Bory-Reyes, “Commutators and singular integral operators in Clifford analysis,” Complex Variables and Elliptic Equations, vol. 50, no. 4, 265 pages, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
27. R. Abreu-Blaya and J. Bory-Reyes, “On the Riemann Hilbert type problems in Clifford analysis,” Advances in Applied Clifford Algebras, vol. 11, no. 1, 15 pages, 2001. View at Zentralblatt MATH · View at MathSciNet
28. R. Abreu-Blaya, D. Peña-Peña, and J. Bory-Reyes, “Clifford Cauchy type integrals on Ahlfors-David regular surfaces in ${ℝ}^{m+1}$,” Advances in Applied Clifford Algebras, vol. 13, no. 2, 133 pages, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
29. R. Abreu-Blaya, J. Bory-Reyes, R. Delanghe, and F. Sommen, “Harmonic multivector fields and the Cauchy integral decomposition in Clifford analysis,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 11, no. 1, 95 pages, 2004. View at Zentralblatt MATH · View at MathSciNet
30. R. Abreu-Blaya, J. Bory-Reyes, and D. Peña-Peña, “Jump problem and removable singularities for monogenic functions,” Journal of Geometric Analysis, vol. 17, no. 1, 1 pages, 2007. View at MathSciNet
31. F. Brackx, R. Delanghe, and F. Sommen, Clifford Analysis, vol. 76 of Research Notes in Mathematics, Pitman, Boston, Mass, USA, 1982. View at Zentralblatt MATH · View at MathSciNet
32. V. Iftimie, “Fonctions hypercomplexes,” Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, vol. 9, no. 57, 279 pages, 1965. View at Zentralblatt MATH · View at MathSciNet
33. R. Abreu-Blaya, J. Bory-Reyes, O. F. Gerus, and M. Shapiro, “The Clifford-Cauchy transform with a continuous density: N. Davydov's theorem,” Mathematical Methods in the Applied Sciences, vol. 28, no. 7, 811 pages, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
34. R. Abreu-Blaya, J. Bory-Reyes, and T. Moreno-García, “Teodorescu transform decomposition of multivector fields on fractal hypersurfaces,” in Wavelets, Multiscale Systems and Hypercomplex Analysis, vol. 167 of Operator Theory: Advances and Applications, p. 1, Birkhäuser, Basel, Switzerland, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
35. R. Abreu-Blaya, J. Bory-Reyes, and T. Moreno-García, “Minkowski dimension and Cauchy transform in Clifford analysis,” Complex Analysis and Operator Theory, vol. 1, no. 3, 301 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
36. R. Abreu-Blaya, J. Bory-Reyes, and T. Moreno-García, “Cauchy transform on nonrectifiable surfaces in Clifford analysis,” Journal of Mathematical Analysis and Applications, vol. 339, no. 1, 31 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
37. R. Abreu-Blaya, J. Bory-Reyes, T. Moreno-García, and D. Peña-Peña, “Weighted Cauchy transforms in Clifford analysis,” Complex Variables and Elliptic Equations, vol. 51, no. 5-6, 397 pages, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
38. J. Bory-Reyes and R. Abreu-Blaya, “Cauchy transform and rectifiability in Clifford analysis,” Zeitschrift für Analysis und ihre Anwendungen, vol. 24, no. 1, 167 pages, 2005. View at Zentralblatt MATH · View at MathSciNet
39. R. Abreu-Blaya, J. Bory-Reyes, R. Delanghe, and F. Sommen, “Cauchy integral decomposition of multi-vector valued functions on hypersurfaces,” Computational Methods and Function Theory, vol. 5, no. 1, 111 pages, 2005. View at Zentralblatt MATH · View at MathSciNet