Singular integrals, harmonic functions, and differentiability properties of functions of several variables

1967 ◽  
pp. 316-335 ◽  
Author(s):  
E. M. Stein
Keyword(s):  
Harmonic Functions ◽  
Singular Integrals ◽  
Several Variables ◽  
Differentiability Properties

scholarly journals On the theory of harmonic functions of several variables: I. The theory of Hp-spaces

1960 ◽  
Vol 103 (1-2) ◽  
pp. 25-62 ◽  
Author(s):  
Elias M. Stein ◽  
Guido Weiss
Keyword(s):  
Harmonic Functions ◽  
Several Variables ◽  
Hp Spaces

scholarly journals Fourier coefficients and growth of harmonic functions

1987 ◽  
Vol 10 (3) ◽  
pp. 443-452 ◽  
Author(s):  
A. fryant ◽  
H. Shankar
Keyword(s):  
Harmonic Functions ◽  
Fourier Coefficients ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Several Variables ◽  
Order And Type ◽  
Necessary And Sufficient

We consider Harmonic Functions,Hof several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so thatHis an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity in terms of its Fourier coefficients in caseHis not entire. Further, we obtain, in terms of its Fourier coefficients, the Order and Type growth measures, both in caseHis entire or non-entire.

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