Transversally Lipschitz harmonic functions are Lipschitz

References

• Pavlović , M . 2007 . Lipschitz conditions on the modulus of a harmonic function . Rev. Mat. Iberoam. , 23 ( 3 ) : 831 – 845 .
   Google Scholar
• Détraz , Jacqueline . 1981 . Classes de Bergman de fonctions harmoniques . Bull. Soc. Math. France , 109 ( 2 ) : 259 – 268 .
   Google Scholar
• Dyakonov , KM . 1997 . Equivalent norms on Lipschitz-type spaces of holomorphic functions . Acta Math. , 178 ( 2 ) : 143 – 167 .
   Google Scholar
• Pavlović , M . 1997 . On K. M. Dyakonov's paper: “Equivalent norms on Lipschitz-type spaces of holomorphic functions” . Acta Math. , 178 ( 2 ) : 143 – 167 . MR1459259 (98g:46029)]. Acta Math. 183(1) (1999), 141–143
   Google Scholar
• Havin , VP . 1971 . A generalization of the Privalov-Zygmund theorem on the modulus of continuity of the conjugate function . Izv. Akad. Nauk Armjan. SSR Ser. Mat. , 6 ( 2–3 ) : 252 – 258 . ibid. 6(4) (1971), 265–287
   Google Scholar
• Zygmund , A . 1959 . Trigonometric Series , 2nd , Vol. I and II , New York : Cambridge University Press .
   Google Scholar
• Ravisankar , S . 2011 . “ Lipschitz properties of harmonic and holomorphic functions ” . In Ph.D. diss. , The Ohio State University .
   Google Scholar
• Herbig , A-K and McNeal , J . 2012 . Convex defining functions for convex domains . J. Geom. Anal. , 22 : 433 – 454 .
   Google Scholar
• Gilbarg , David and Trudinger , NS . 1983 . Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 2nd ed., Vol. 224 , Berlin : Springer-Verlag .
   Google Scholar