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Sharp Geometric Poincare Inequalities for Vector Fields and Non-Doubling Measures |
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| Authors: | Franchi Bruno; Perez Carlos; Wheeden Richard L |
| Institution: | Dipartimento di Matematica, Università di Bologna Piazza di Porta, S. Donato 5 I-40127, Bologna, Italy, franchib{at}dm.unibo.it Departamento de Matemáticas, Universidad Autónoma de Madrid 28049, Madrid, Spain, carlos.perez{at}uam.es Department of Mathematics, Rutgers University 110 Frelinghuysen Road, Piscataway, NJ 08854-8019 USA wheeden{at}math.rutgers.edu |
| Abstract: | We derive Sobolev–Poincaré inequalities that estimatethe Lq(d µ) norm of a function on a metric ball when µis an arbitrary Borel measure. The estimate is in terms of theL1(d  ) norm on the ball of a vector field gradient of the function,where d dx is a power of a fractional maximal function of µ.We show that the estimates are sharp in several senses, andwe derive isoperimetric inequalities as corollaries. 1991 MathematicsSubject Classification: 46E35, 42B25. |
| Keywords: | Sobolev-Poincaré inequalities fractional maximal functions isoperimetric estimates vector field gradients non-doubling measures weight functions |
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