Chapter IX: Ap Weights - ScienceDirect The chapter discusses the necessary conditions—it assumes a constant k = k p,μ independent of f such that for some p, 1 ≤ p < ∞, and all f ɛ L p μ (R n) and λ > 0 A p is necessary for the Hardy–Littlewood maximal operator M to map L p μ (R n) into wk- L p μ (R n)
Exponent Sets and Muckenhoupt Ap-weights - DiVA In the study of the weighted -Laplace equation, it is often important to acquire good estimates of capacities One useful tool for finding such estimates in metric spaces is exponent sets, which are sets describing the local dimensionality of the measure asso-ciated with the space In this thesis, we limit ourselves to the weighted
Factorization of A lt;sub gt;p lt; sub gt; Weights A positive weight w on [0, 1] is in dyadic AP, 1 < p < C<, if w satisfies condition (1 1) where the supremum is taken over all dyadic intervals I Similarly, w is in dyadic Al if w satisfies conditions (1 2) where the supremum is taken over all dyadic intervals I In this section we will show that if w is in dyadic AP, then W = w1(w2) P
arXiv:1706. 02620v1 [math. CA] 8 Jun 2017 Given 1 < p < ∞, a weight w is in the Muckenhoupt class Ap, denoted by w ∈ Ap, if 0 < w(x) < ∞ a e and [w]Ap = sup Q − Z Q wdx − Z Q w1−p′ dx p−1 < ∞, where the supremum is taken over all cubes Q Since p′ − 1 = p′ p, we can also write the Ap condition in an equivalent form using Lp and Lp′ norms: for any cube Q, (2 1
Ap Weights in Directionally (γ,m) Limited Space and Applications - MDPI Let (X,d) be a directionally (γ,m)-limited space with every γ∈(0,∞) In this setting, we aim to study an analogue of the classical theory of Ap(μ) weights As an application, we establish some weighted estimates for the Hardy–Littlewood maximal operator
Chapter 2 Muckenhoupt weights - Springer For weights with only one singularity, we establish a criterion for their membership in Ap(f) in terms of the W transform It is this criterion which will enable us to identify plenty of oscillating weights as Muckenhoupt weights Let f be a composed locally rectifiable curve
Weight - Wikipedia In science and engineering, the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition [1] [2] [3] Some standard textbooks [4] define weight as a vector quantity, the gravitational force acting on