منابع مشابه
Uniform Rectifiability, Carleson Measure Estimates, and Approximation of Harmonic Functions
Let E ⊂ Rn+1, n ≥ 2, be a uniformly rectifiable set of dimension n. Then bounded harmonic functions in Ω := Rn+1 \ E satisfy Carleson measure estimates, and are “ε-approximable”. Our results may be viewed as generalized versions of the classical F. and M. Riesz theorem, since the estimates that we prove are equivalent, in more topologically friendly settings, to quantitative mutual absolute con...
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In this paper we offer a new definition of monogenicity for functions defined on R with values in the Clifford algebra Rn following an idea inspired by the recent papers [6], [7]. This new class of monogenic functions contains the polynomials (and, more in general, power series) with coefficients in the Clifford algebra Rn. We will prove a Cauchy integral formula as well as some of its conseque...
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Since 1970’s B. Fuglede and others have been studying finely holomorhic functions, i.e., ‘holomorphic’ functions defined on the so-called fine domains which are not necessarily open in the usual sense. This note is a survey of finely monogenic functions which were introduced in [12] like a higher dimensional analogue of finely holomorphic functions.
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Monogenic functions are basic to Clifford analysis. On Euclidean space they are defined as smooth functions with values in the corresponding Clifford algebra satisfying a certain system of first order differential equations, usually referred to as the Dirac equation. There are two equally natural extensions of these equations to a Riemannian spin manifold only one of which is conformally invari...
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and Applied Analysis 3 2. Main Results and Proofs Lemma 2.1. For α α1, . . . , αn ∈ D, let uα z1, . . . , zn ∏n j 1 1 − |αj |2 / 1 − αjzj . Then uα z1, . . . , zn ∈ Lφa D , and ‖uα z ‖σn ≤ 1 φ−1 ∏n j 1 ( 1/δ2 j )) . 2.1 Proof. It is easy to see that ‖uα z ‖∞ ∏n j 1 1 |αj | / 1 − |αj | 2 ∏n j 1 2 − δj /δj . Since φ 0 0, the convexity of φ implies φ ax ≤ aφ x for 0 ≤ a ≤ 1. Hence, for every C > 0...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2007
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm180-1-2