Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions
نویسندگان
چکیده
منابع مشابه
Weighted Weak Type Inequalities for the Hardy Operator When
The paper studies the weighted weak type inequalities for the Hardy operator as an operator from weighted L to weighted weak L in the case p = 1. It considers two different versions of the Hardy operator and characterizes their weighted weak type inequalities when p = 1. It proves that for the classical Hardy operator, the weak type inequality is generally weaker when q < p = 1. The best consta...
متن کاملWeighted Weak-type Inequalities for the Maximal Function of Nonnegative Integral Transforms over Approach Regions
The relation between approach regions and singularities of nonnegative kernels Kt(x, y) is studied, where t ∈ (0,∞), x, y ∈ X, and X is a homogeneous space. For 1 ≤ p < q < ∞, a sufficient condition on approach regions Ωa (a ∈ X) is given so that the maximal function sup (x,t)∈Ωa ∫ X Kt(x, y)f(y) dσ(y) is weak-type (p, q) with respect to a pair of measures σ and ω. It is shown that this conditi...
متن کاملSome Hardy Type Inequalities with Weighted Functions via Opial Type Inequalities
In this paper, we will prove several new inequalities of Hardy type with explicit constants. The main results will be proved using generalizations of Opial's inequality.
متن کاملCarleman type inequalities and Hardy type inequalities for monotone functions
This Ph.D. thesis deals with various generalizations of the inequalities by Carleman, Hardy and Pólya-Knopp. In Chapter 1 we give an introduction and overview of the area that serves as a frame for the rest of the thesis. In Chapter 2 we consider Carleman’s inequality, which may be regarded as a discrete version of Pólya-Knopp’s inequality and also as a natural limiting inequality of the discre...
متن کاملHardy-type inequalities for integral transforms associated with Jacobi operator
We establish Hardy-type inequalities for the Riemann-Liouville and Weyl transforms associated with the Jacobi operator by using Hardy-type inequalities for a class of integral operators.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1982
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-72-1-9-26