Efficient Computation of Fourier Transforms on Compact Groups.
We prove that peak shaped eigenfunctions of the one-dimensional uncentered Hardy-Littlewood maximal operator are symmetric and homogeneous. This implies that the norms of the maximal operator on L(p) spaces are not attained.
We consider elementary operators , acting on a unital Banach algebra, where and are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families and , i.e. (), where all and ( and ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class of functions...
In this paper, we rule out the possibility that a certain method of proof in the sums differences conjecture can settle the Kakeya Conjecture.
For two strictly elliptic operators L₀ and L₁ on the unit ball in ℝⁿ, whose coefficients have a difference function that satisfies a Carleson-type condition, it is shown that a pointwise comparison concerning Lusin area integrals is valid. This result is used to prove that if L₁u₁ = 0 in B₁(0) and then lies in the exponential square class whenever L₀ is an operator so that L₀u₀ = 0 and implies is in the exponential square class; here S is the Lusin area integral. The exponential square theorem,...
A sharp embedding relation between local Hardy spaces and modulation spaces is given.