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    STUDIA MATHEMATICA - Issue no. 4 / 2010  
         
  Article:   BOOK REVIEWS: STEVEN G. KRANTZ, EXPLORATIONS IN HARMONIC ANALYSIS- WITH APPLICATIONS TO COMPLEX FUNCTION THEORY AND THE HEISENBERG GROUP, XIV+360 PP, APPLIED AND NUMERICAL HARMONIC ANALYSIS, BIRKHÄUSER, BOSTON -BASEL - BERLIN, 2009, ISBN: 978-0-8176-4668.

Authors:  GABRIELA KOHR. 		 
       
         
  Abstract:  This is a self-contained introduction to modern harmonic analysis, starting with the classical theory of Fourier series and culminating in the theory of pseudodifferential operators and analysis on Heisenberg group. The idea of studying harmonic analysis on Heisenberg group (fractional integrals and singular integrals) belongs to E. M. Stein and his school in the 1970s. This turned out to be a powerful device for developing sharp estimates for integral operators (the Bergman projections, the Szegö projections) that arise naturally in the several complex variable setting. (A chapter of the book is dedicated to a crash course in several complex variables).  
         
     
         
         
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