Harmonic Functions, Conjugate Harmonic Functions and the Hardy Space $$H^1$$ H 1 in the Rational Dunkl Setting
نویسندگان
چکیده
منابع مشابه
[hal-00864457, v1] The Hardy space H1 in the rational Dunkl setting
This paper consists in a first study of the Hardy space H in the rational Dunkl setting. Following Uchiyama’s approach, we characterizee H atomically and by means of the heat maximal operator. We also obtain a Fourier multiplier theorem for H. These results are proved here in the one-dimensional case and in the product case.
متن کاملConjugate Harmonic Functions and Clifford Algebras
We generalize a Hardy-Littlewood inequality and a Privalov inequality for conjugate harmonic functions in the plane to components of Clifford-valued monogenic functions.
متن کاملA lower estimate of harmonic functions
We shall give a lower estimate of harmonic functions of order greater than one in a half space, which generalize the result obtained by B. Ya. Levin in a half plane.
متن کاملOn the conjugate of periodic piecewise harmonic functions
The paper considers the conjugate of periodic functions which are piecewise harmonic. In particular, we consider the harmonic conjugate of the solution of the problem of stationary heat conduction through a periodic network of fibres and matrix of arbitrary shape. A numerical example is also presented.
متن کاملOn the Number of Zeros of Certain Rational Harmonic Functions
Extending a result of Khavinson and Świa̧tek (2003) we show that the rational harmonic function r(z) − z, where r(z) is a rational function of degree n > 1, has no more than 5n − 5 complex zeros. Applications to gravitational lensing are discussed. In particular, this result settles a conjecture by Rhie concerning the maximum number of lensed images due to an n-point gravitational lens.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2019
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-019-09666-0