Cover Image

Hardy Inequalities on Homogeneous Groups : 100 Years of Hardy Inequalities.

Bibliographic Details
Main Author: Ruzhansky, Michael.
Other Authors: Suragan, Durvudkhan.
Format: eBook
Language:English
Published: Cham : Springer International Publishing AG, 2019.
Edition:1st ed.
Series:Progress in Mathematics Series
Subjects:
Electronic books.
Online Access:Click to View
Table of Contents:
  • Intro
  • Contents
  • Preface
  • Introduction
  • Chapter 1: Analysis on Homogeneous Groups
  • Homogeneous groups
  • Properties of homogeneous groups
  • Homogeneous quasi-norms
  • Polar coordinates
  • Convolutions
  • Polynomials
  • Radial and Euler operators
  • Radial derivative
  • Euler operator
  • From radial to non-radial inequalities
  • Euler semigroup e-tE*E
  • Stratified groups
  • Stratified Lie groups
  • Extended sub-Laplacians
  • Divergence theorem
  • Green's identities for sub-Laplacians
  • Green's identities for p-sub-Laplacians
  • Sub-Laplacians with drift
  • Polarizable Carnot groups
  • Heisenberg group
  • Quaternionic Heisenberg group
  • H-type groups
  • Chapter 2: Hardy Inequalities on Homogeneous Groups
  • Hardy inequalities and sharp remainders
  • Hardy inequality and uncertainty principle
  • Weighted Hardy inequalities
  • Hardy inequalities with super weights
  • Hardy inequalities of higher order with super weights
  • Two-weight Hardy inequalities
  • Critical Hardy inequalities
  • Critical Hardy inequalities
  • Another type of critical Hardy inequality
  • Critical Hardy inequalities of logarithmic type
  • Remainder estimates
  • Remainder estimates for Lp-weighted Hardy inequalities
  • Critical and subcritical Hardy inequalities
  • A family of Hardy-Sobolev type inequalities on quasi-balls
  • Improved Hardy inequalities on quasi-balls
  • Stability of Hardy inequalities
  • Stability of Hardy inequalities for radial functions
  • Stability of Hardy inequalities for general functions
  • Stability of critical Hardy inequality
  • Chapter 3: Rellich, Caffarelli-Kohn-Nirenberg, and Sobolev Type Inequalities
  • Rellich inequality
  • Rellich type inequalities in L2
  • Rellich type inequalities in Lp
  • Stability of Rellich type inequalities
  • Higher-order Hardy-Rellich inequalities
  • Sobolev type inequalities.
  • Hardy and Sobolev type inequalities
  • Weighted Lp-Sobolev type inequalities
  • Stubbe type remainder estimates
  • Caffarelli-Kohn-Nirenberg inequalities
  • Lp-Caffarelli-Kohn-Nirenberg inequalities
  • Higher-order Lp-Caffarelli-Kohn-Nirenberg inequalities
  • New type of Lp-Caffarelli-Kohn-Nirenberg inequalities
  • Extended Caffarelli-Kohn-Nirenberg inequalities
  • Chapter 4: Fractional Hardy Inequalities
  • Gagliardo seminorms and fractional p-sub-Laplacians
  • Fractional Hardy inequalities on homogeneous groups
  • Fractional Sobolev inequalities on homogeneous groups
  • Fractional Gagliardo-Nirenberg inequalities
  • Fractional Caffarelli-Kohn-Nirenberg inequalities
  • Lyapunov inequalities on homogeneous groups
  • Lyapunov type inequality for fractional p-sub-Laplacians
  • Lyapunov type inequality for systems
  • Lyapunov type inequality for Riesz potentials
  • Hardy inequalities for fractional sub-Laplacians on stratified groups
  • Riesz kernels on stratified Lie groups
  • Hardy inequalities for fractional powers of sub-Laplacians
  • Landau-Kolmogorov inequalities on stratified groups
  • Chapter 5: Integral Hardy Inequalities on Homogeneous Groups
  • Two-weight integral Hardy inequalities
  • Convolution Hardy inequalities
  • Hardy-Littlewood-Sobolev inequalities on homogeneous groups
  • Maximal weighted integral Hardy inequality
  • Chapter 6: Horizontal Inequalities on Stratified Groups
  • Horizontal Lp-Caffarelli-Kohn-Nirenberg inequalities
  • Badiale-Tarantello conjecture
  • Horizontal higher-order versions
  • Horizontal Hardy and Rellich inequalities
  • Critical horizontal Hardy type inequality
  • Two-parameter Hardy-Rellich inequalities by factorization
  • Hardy-Rellich type inequalities and embedding results
  • Horizontal Sobolev type inequalities
  • Horizontal extended Caffarelli-Kohn-Nirenberg inequalities.
  • Horizontal Hardy-Rellich type inequalities for p-sub-Laplacians
  • Inequalities for weighted p-sub-Laplacians
  • Horizontal Rellich inequalities for sub-Laplacians with drift
  • Horizontal anisotropic Hardy and Rellich inequalities
  • Horizontal Picone identities
  • Horizontal anisotropic Hardy type inequality
  • Horizontal anisotropic Rellich type inequality
  • Horizontal Hardy inequalities with multiple singularities
  • Horizontal many-particle Hardy inequality
  • Hardy inequality with exponential weights
  • Chapter 7: Hardy-Rellich Inequalities and Fundamental Solutions
  • Weighted Lp-Hardy inequalities
  • Weighted Lp-Rellich inequalities
  • Two-weight Hardy inequalities and uncertainty principles
  • Rellich inequalities for sub-Laplacians with drift
  • Hardy inequalities on the complex affine group
  • Hardy inequalities for Baouendi-Grushin operators
  • Weighted Lp-inequalities with boundary terms
  • Hardy and Caffarelli-Kohn-Nirenberg inequalities
  • Rellich inequalities
  • Chapter 8: Geometric Hardy Inequalities on Stratified Groups
  • L2-Hardy inequality on the half-space
  • Examples of Heisenberg and Engel groups
  • Lp-Hardy inequality on the half-space
  • L2-Hardy inequality on convex domains
  • Lp-Hardy inequality on convex domains
  • Chapter 9: Uncertainty Relations on Homogeneous Groups
  • Abstract position and momentum operators
  • Definition and assumptions
  • Examples
  • Position-momentum relations
  • Further position-momentum identities
  • Heisenberg-Kennard and Pythagorean inequalities
  • Euler-Coulomb relations
  • Heisenberg-Pauli-Weyl uncertainty principle
  • Radial dilations - Coulomb relations
  • Further weighted uncertainty type inequalities
  • Chapter 10: Function Spaces on Homogeneous Groups
  • Euler-Hilbert-Sobolev spaces
  • Poincaré type inequality
  • Sobolev-Lorentz-Zygmund spaces
  • Generalized Morrey spaces.
  • Bessel-Riesz kernels on homogeneous groups
  • Hardy-Littlewood maximal operator in Morrey spaces
  • Bessel-Riesz operators in Morrey spaces
  • Generalized Bessel-Riesz operators
  • Olsen type inequalities for Bessel-Riesz operator
  • Fractional integral operators in Morrey spaces
  • Olsen type inequalities for fractional integral operators
  • Summary of results
  • Besov type space: Gagliardo-Nirenberg inequalities
  • Generalized Campanato spaces
  • Chapter 11: Elements of Potential Theory on Stratified Groups
  • Boundary value problems on stratified groups
  • Layer potentials of the sub-Laplacian
  • Single layer potentials
  • Double layer potential
  • Traces and Kac's problem for the sub-Laplacian
  • Traces of Newton potential for the sub-Laplacian
  • Powers of the sub-Laplacian
  • Extended Kohn Laplacians on the Heisenberg group
  • Powers of the Kohn Laplacian
  • Hardy inequalities with boundary terms on stratified groups
  • Green functions on H-type groups
  • Green functions and Dirichlet problem in wedge domains
  • Green functions and Dirichlet problem in strip domains
  • p-sub-Laplacian Picone's inequality and consequences
  • Chapter 12: Hardy and Rellich Inequalities for Sums of Squares
  • Assumptions
  • Examples
  • Divergence formula
  • Green's identities for sums of squares
  • Consequences of Green's identities
  • Differential forms, perimeter and surface measures
  • Local Hardy inequalities
  • Anisotropic Hardy inequalities via Picone identities
  • Local uncertainty principles
  • Local Rellich inequalities
  • Rellich inequalities via Picone identities
  • Bibliography
  • Index.

Similar Items