Lacunary series in quaternion B^p,q spaces

References

• Anderson , J , Clunie , J and Pommerenke , Ch . 1974 . On Bloch functions and normal functions . J. Reine Angew. Math. , 270 : 12 – 37 .
   Web of Science ®Google Scholar
• Stroethoff , K . 1989 . Besov-type characterisations for the Bloch space . Bull. Aust. Math. Soc. , 39 : 405 – 420 .
   Web of Science ®Google Scholar
• Kwon , EG , Shim , OH and Bae , EK . 2006 . A characterization of Bloch function . Commun. Korean Math. Soc. , 21 ( 2 ) : 287 – 292 .
   Google Scholar
• Cnops , J and Delanghe , R . 2000 . Möbius invariant spaces in the unit ball . Appl. Anal. , 73 ( 1–2 ) : 45 – 64 .
   Google Scholar
• Gürlebeck , K , Kähler , U , Shapiro , M and Tovar , LM . 1999 . On Q p -spaces of quaternion-valued functions . Complex Variables, Theory Appl. , 39 : 115 – 135 .
   Google Scholar
• El-Sayed Ahmed , A . 2008 . On weighted α−Besov spaces and α−Bloch spaces of quaternion-valued functions . Numer. Funct. Anal. Optim. , 29 : 1064 – 1081 .
   Web of Science ®Google Scholar
• Bernstein , S and Cerejeiras , P . 2007 . Carleson measure and monogenic functions . Stud. Math. , 180 ( 1 ) : 11 – 25 .
   Web of Science ®Google Scholar
• Bernstein , S , Gürlebeck , K , Reséndis , LF and Tovar , LM . 2006 . Dirichlet and Hardy spaces of harmonic and monogenic functions . Z. Anal. Anwend. , 24 ( 4 ) : 763 – 789 .
   Web of Science ®Google Scholar
• Bernstein , S , Gürlebeck , K , Reséndis , LF and Tovar , LM . 2004 . “ B p,q -functions and their harmonic majorants ” . In Trends in Mathematics Advances in Analysis and Geometry , Edited by: Qian , Tao . 51 – 63 . Basel, , Switzerland : Birkhäuser Verlarg Publisher .
   Google Scholar
• Gürlebeck , K and El-Sayed Ahmed , A . 2003 . “ Integral norms for hyperholomorphic Bloch-functions in the unit ball of ℝ3 ” . In Progress in Analysis , Edited by: et al. , Begehr . Vol. I , 253 – 263 . River Edge, NJ : Kluwer Academic Publishers .
   Google Scholar
• Gürlebeck , K and El-Sayed Ahmed , A . 2004 . “ On series expansions of hyperholomorphic B q functions ” . In Trends in Mathematics Advances in Analysis and Geometry , Edited by: Qian , Tao . 113 – 129 . Basel, , Switzerland : Birkhäuser Verlarg Publisher .
   Google Scholar
• Gürlebeck , K and El-Sayed Ahmed , A . 2004 . “ On B q spaces of hyperholomorphic functions and the Bloch space in ℝ3 ” . In finite or infinite complex Analysis and its applications, Adv. Complex Analysis and applications , Edited by: Hung Son , Le . 269 – 286 . Boston, MA : Kluwer Academic Publishers .
   Google Scholar
• Gürlebeck , K and Malonek , HR . 2001 . On strict inclusions of weighted Dirichlet spaces of monogenic functions . Bull. Aust. Math. Soc. , 64 : 33 – 50 .
   Web of Science ®Google Scholar
• Miao , J . 1992 . A property of analytic functions with Hadamard gaps . Bull. Aust. Math. Soc. , 45 : 105 – 112 .
   Web of Science ®Google Scholar
• Reséndis , LF and Tovar , LM . 2004 . “ Besov-type characterizations for Quaternionic Bloch functions ” . In Finite or Infinite Complex Analysis and its Applications, Advances in Complex Analysis and applications , Edited by: Hung Son , Le . 207 – 220 . Boston, MA : Kluwer Academic Publishers .
   Google Scholar
• El-Sayed Ahmed , A , Gürlebeck , K , Reséndis , LF and Tovar , LM . 2006 . Characterizations for the Bloch space by B p,q spaces in Clifford analysis . Complex Var. Elliptic Equ. , 51 : 119 – 136 .
   Google Scholar
• Brackx , F , Chisholm , JSR and Soucek , V . 2001 . Clifford Analysis and its Applications , Dordrecht, Boston, London : Kluwer Academic Publishers .
   Google Scholar
• Brackx , F , Delanghe , R and Sommen , F . 1982 . Clifford Analysis , Boston, London, Melbourne : Pitman Research Notes in Math. .
   Google Scholar
• Gürlebeck , K , Habetha , K and Sprößig , W . 2008 . Holomorphic Functions in the Plane and n-dimensional Space , Vol. xiii , Basel, , Switzerland : Birkhäuser Verlarg Publisher .
   Google Scholar
• Gürlebeck , K and Sprößig , W . 1997 . Quaternionic and Clifford Calculus for Engineers and Physicists , Chichester : John Wiley &. Sons .
   Google Scholar
• Kravchenko , VV and Shapiro , MV . 1996 . Integral representations for spatial models of mathematical physics , Longman : Pitman Research Notes in Mathematics Series 351, Harlow .
   Google Scholar
• Mateljevic , M and Pavlovic , M . 1983 . L p -behavior of power series with positive coefficients and Hardy spaces . Proc. Amer. Math. Soc. , 87 ( 2 ) : 309 – 316 .
   Web of Science ®Google Scholar
• Malonek , M . 1990 . Power series representation for monogenic functions in ℝ m+1 based on a permutational product . Complex Variables Theory Appl. , 15 : 181 – 191 .
   Google Scholar
• Baernstein , A . 1980 . “ Analytic Functions of Bounded Mean Oscillation II ” . In in Aspects of Contemporary Complex Analysis , 3 – 36 . London : Academic Press .
   Google Scholar
• Palmberg , N . 2007 . Composition operators acting on 𝒩 p -spaces . Bull. Belg. Math. Soc. Simon Stevin. , 14 : 545 – 554 .
   Web of Science ®Google Scholar
• Wulan , H and Zhu , K . 2007 . Lacunary series in 𝒬 K spaces . Stud. Math. , 178 : 217 – 230 .
   Web of Science ®Google Scholar
• Yamashita , S . 1980 . Gap series and α-Bloch functions . Yokohama Math. J. , 28 : 31 – 36 .
   Google Scholar
• Avetsiyan , A . 2007 . Hardy-Bloch type spaces and lacunary series in the polydisk . Glasg. Math. J. , 49 ( 2 ) : 345 – 356 .
   Google Scholar
• Stević , S . 2006 . A generalization of a result of Choa on analytic functions with Hadamard gaps . J. Korean Math. Soc. , 43 ( 3 ) : 579 – 591 .
   Web of Science ®Google Scholar
• Stević , S . 2007 . On Bloch-type functions with Hadamard gaps . Abstr. Appl. Anal. , 2007 : 8 (Article ID 39176)
   Google Scholar
• Aulakari , R , Stegenga , D and Xiao , J . 1996 . Some subclasses of BMOA and their characterization in terms of Carleson measures . Rocky Mt. J. Math. , 26 : 485 – 506 .
   Web of Science ®Google Scholar