Titlebook: Geometric Aspects of Harmonic Analysis; Paolo Ciatti,Alessio Martini Conference proceedings 2021 The Editor(s) (if applicable) and The Aut

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pessimism

Potential Spaces on Lie Groups,f a sub-Laplacian with drift. The sub-Laplacian is written as the (negative) sum of squares of a collection of left-invariant vector fields satisfying H?rmander’s condition. These spaces were recently introduced by the authors. In this paper we prove a norm characterization in terms of finite differ

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On Fourier Restriction for Finite-Type Perturbations of the Hyperbolic Paraboloid,=?., which are of the form .?=?.?+?.(.), where .(.) is a smooth function of finite type. Our results build on previous joint work in which we have studied the case .(.)?=?..∕3 by means of the bilinear method. As it turns out, the understanding of that special case becomes also crucial for the treatm

CAB

,On Young’s Convolution Inequality for Heisenberg Groups,luding Heisenberg groups, the optimal constant in this inequality is equal to that for Euclidean space of the same topological dimension, yet no functions attain exact equality. We characterize ordered pairs of functions that nearly achieve equality for Heisenberg groups. The analysis relies on a ch

難聽的聲音

Strongly Singular Integrals on Stratified Groups,an oscillatory factor. Oscillating multipliers have been examined extensively in the Euclidean setting where sharp, endpoint .. estimates are well known. In the Lie group setting, corresponding .. bounds for oscillating spectral multipliers have been established by several authors but only in the op

Kernel

,On the Restriction of Laplace–Beltrami Eigenfunctions and Cantor-Type Sets,functions of . when restricted to certain fractal subsets Γ of .. The proofs in their entirety appear in Eswarathasan and Pramanik (Restriction of Laplace–Beltrami eigenfunctions to random Cantor-type sets on manifolds, 2019). The sets Γ that we consider are random and of Cantor-type. For large Lebe

Kernel

Basis Properties of the Haar System in Limiting Besov Spaces,tive results for ., and providing new counterexamples in other situations. The study is based on suitable estimates of the dyadic averaging operators .; in particular we find asymptotically optimal growth rates for the norms of these operators in global and local situations.

饒舌的人

Obstacle Problems Generated by the Estimates of Square Function,n this article the estimates of the type ∥.∥.?≤?..∥.∥., .?≥?2, were considered for the dyadic square function operator ., and Davis found the sharp values of constants ... However, along with the sharp constants one can consider a more subtle characteristic of the above estimate. This quantity is ca

inventory

Of Commutators and Jacobians, multiplication operators with singular integrals in general, and with the Beurling operator in particular. A conjecture of T. Iwaniec regarding the solvability for general datum . remains open, but recent partial results in this direction will be presented. These are based on a complete characteris

BYRE

Paolo Ciatti,Alessio MartiniA recent updated state of the art in harmonic analysis.Real variable and combinatorial methods in Fourier analysis.A wide range of topics related to geometric analysis and several complex variables