Sobolev inequalities: isoperimetry and symmetrization

• Autores: Walter Andrés Ortiz Vargas
• Directores de la Tesis: Joaquim Martín Pedret (dir. tes.)
• Lectura: En la Universitat Autònoma de Barcelona ( España ) en 2019
• Idioma: español
• Tribunal Calificador de la Tesis: Maria Rosaria Posteraro (presid.), Joan Orobitg i Huguet (secret.), Santiago Boza Rocho (voc.)
• Programa de doctorado: Programa de Doctorado en Matemáticas por la Universidad Autónoma de Barcelona
• Materias:
  • Matemáticas
• Enlaces
  • Tesis en acceso abierto en: TESEO
• Resumen

  • The first part of the thesis is devoted to obtain a Sobolev type embedding result for Besov spaces defined on a doubling metric space. This will be done by obtaining pointwise estimates between the special difference (called oscillation of and the X−modulus of smoothness defined by EX(f,r) ∶= ∥∫−B(x,r) ∣f(x) − f(y)∣dµ(y)∥X .

    is the decreasing rearrangement of for all t > 0 and X a rearrangement invariant space on Ω.

    In the second part of the thesis, to obtain symmetrization inequalities on probability metric spaces that admit a convex isoperimetric estimator which incorporate in their formulation the isoperimetric estimator and that can be applied to provide a unified treatment of sharp Sobolev-Poincar´e and Nash type inequalities.