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Se construyen dos bases incondicionales de L2(R) adaptadas al estudio de la integral de Cauchy sobre una curva cuerda-arco, y se extiende la construcción a L2(Rd). Esto permite obtener una prueba simple del "Teorema T(b)" de G. David, J.L. Journé u S. Semmes. Se define un espacio de Hardy ponderado Hb1(Rd) caracterizado por las bases anteriores. Finalmente se aplican estos métodos al estudio del potencial de doble capa sobre una superficie lipschitziana.
Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces are no longer valid in larger spaces. However, when a function f is in some sense close to a Bernstein space, then the corresponding relation holds with a remainder or error term. This paper presents a new, unified approach to these errors in terms of the distance of f from . The difficult situation of derivative-free error estimates is also covered.
Let Γ be a compact d-set in ℝⁿ with 0 < d ≤ n, which includes various kinds of fractals. The author shows that the Besov spaces defined by two different and equivalent methods, namely, via traces and quarkonial decompositions in the sense of Triebel are the same spaces as those obtained by regarding Γ as a space of homogeneous type when 0 < s < 1, 1 < p < ∞ and 1 ≤ q ≤ ∞.
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