The Stieltjes integrals in the theory of harmonic functions
    
    
  
  
  
      
      
      
        
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 151-168
    
  
  
  
  
  
    
      
      
        
      
      
      
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              			We study various Stieltjes integrals, such as Poisson–Stieltjes, conjugate Poisson–Stieltjes, Schwartz–Stieltjes and Cauchy–Stieltjes, and prove theorems on the existence of their finite angular limits a.e. in terms of the Hilbert–Stieltjes integral. These results are valid for arbitrary bounded integrands that are differentiable a.e. and, in particular, for integrands of the class $\mathcal{CBV}$ (countably bounded variation).
			
            
            
            
          
        
      @article{ZNSL_2018_467_a13,
     author = {V. Ryazanov},
     title = {The {Stieltjes} integrals in the theory of harmonic functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {151--168},
     publisher = {mathdoc},
     volume = {467},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a13/}
}
                      
                      
                    V. Ryazanov. The Stieltjes integrals in the theory of harmonic functions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 151-168. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a13/