인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

Introduction What are Poincare and Sobolev inequalities? Poincare inequalities, pointwise estimates, and Sobolev classes Examples and necessary conditions Sobolev type inequalities by means of Riesz potentials Trudinger inequality A version of the Sobolev embedding theorem on spheres Rellich-Kondrachov Sobolev classes in John domains Poincare inequality: examples Carnot-Caratheodory spaces Graphs Applications to PDE and nonlinear potential theory Appendix References.

Sobolev met Poincaré

Concrete mathematics, a foundation for computer science, by Ronald L. Graham, Donald E. Knuth and Oren Patashnik. Pp 625. £24·95. 1989. ISBN 0-201-14236-8 (Addison-Wesley)

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Variable Lebesgue Spaces

Mass und Integral und ihre Algebraisierung Von Prof C Caratheodory Herausgegeben von P Finsler, A Rosenthal und R Steuerwald (Lehrbucher und Monographien aus dem Gebiete der Exakten Wissenschaften Mathematische Reihe, Band 10) Pp 337 (Basel und Stuttgart: Birkhauser Verlag, 1956) 3850 francs; 3850 DM

Measure and Integral

http://grupo.us.es/anaresba/trabajos/carlosperez/1preprint.pdf

New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory

We show that many classical operators in harmonic analysis|such as maximal operators, singular integrals, commutators and fractional integrals|are bounded on the variable Lebesgue space L p( ) whenever the Hardy{Littlewood maximal operator is bounded on L p( ) . Further, we show that such operators satisfy vector-valued inequalities. We do so by applying the theory of weighted norm inequalities and extrapolation. As applications we prove the Calder on{Zygmund inequality for solutions of 4u = f in variable Lebesgue spaces, and prove the Calder on extension theorem for variable Sobolev spaces.

The boundedness of classical operators on variable L-p spaces

Endpoint Estimates for Commutators of Singular Integral Operators

We improve on several weighted inequalities of recent interest by replacing a part of the Ap bounds by weaker A∞ estimates involving Wilson’s A∞ constant [ w ] A ∞ ′ : = sup Q 1 w ( Q ) ∫ Q M ( w χ Q ) . In particular, we show the following improvement of the first author’s A2 theorem for Calderon–Zygmund operators T: ∥ T ∥ ℬ ( L 2 ( w ) ) ≤ c T [ w ] A 2 1 ∕ 2 ( [ w ] A ∞ ′ + [ w − 1 ] A ∞ ′ ) 1 ∕ 2 . Corresponding Ap type results are obtained from a new extrapolation theorem with appropriate mixed Ap-A∞ bounds. This uses new two-weight estimates for the maximal function, which improve on Buckley’s classical bound. We also derive mixed A1-A∞ type results of Lerner, Ombrosi and Perez (2009) of the form ∥ T ∥ ℬ ( L p ( w ) ) ≤ c p p ′ [ w ] A 1 1 ∕ p ( [ w ] A ∞ ′ ) 1 ∕ p ′ , 1 < p < ∞ , ∥ T f ∥ L 1 , ∞ ( w ) ≤ c [ w ] A 1 log ( e + [ w ] A ∞ ′ ) ∥ f ∥ L 1 ( w ) . An estimate dual to the last one is also found, as well as new bounds for commutators of singular integrals.

/pdf/sharp-weighted-bounds-involving-a-3ugkjiqjth.pdf

Sharp weighted bounds involving A

Preface.- Preliminaries.- Part I. One-Weight Extrapolation.- Chapter 1. Introduction to Norm Inequalities and Extrapolation.- Chapter 2. The Essential Theorem.- Chapter 3. Extrapolation for Muckenhoupt Bases.- Chapter 4. Extrapolation on Function Spaces.- Part II. Two-Weight Factorization and Extrapolation.- Chapter 5. Preliminary Results.- Chapter 6. Two-Weight Factorization.- Chapter 7. Two-Weight Extrapolation.- Chapter 8. Endpoint and A1 Extrapolation.- Chapter 9. Applications of Two-Weight Extrapolation.- Chapter 10. Further Applications of Two-Weight Extrapolation.- Appendix A. The Calderon-Zygmund Decomposition.- Bibliography.- Index.

Carlos Pérez

Papers

New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory

The boundedness of classical operators on variable L-p spaces

Endpoint Estimates for Commutators of Singular Integral Operators

Sharp weighted bounds involving A

Weights, Extrapolation and the Theory of Rubio de Francia