Weighted norm inequalities for the Hankel- and -transformations

1986 ◽  
Vol 103 (3-4) ◽  
pp. 325-333 ◽  
Author(s):  
S. A. Emara ◽  
H. P. Heinig
Keyword(s):  
Interpolation Theorem ◽  
Linear Operators ◽  
Weight Functions ◽  
Weighted Estimate ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Hankel Transformation ◽  
Negative Weight ◽  
Marcinkiewicz Interpolation Theorem ◽  
Image Position

SynopsisWe give conditions on pairs of non-negative weight functions u and v which are sufficient that, for 1<p, q <∞,where T is the Hankel-or the K-transformation.The proofs are based on a weighted Marcinkiewicz interpolation theorem for linear operators. In the case that T is the Hankel transformation and 1<p≦q <∞, the result is similar to a weighted estimate of Heywood and Rooney [9], but with different weight conditions.

A weighted norm inequality for the Hankel transformation

1984 ◽  
Vol 99 (1-2) ◽  
pp. 45-50 ◽  
Author(s):  
P. Heywood ◽  
P. G. Rooney
Keyword(s):  
Fourier Transformation ◽  
Norm Inequality ◽  
Weight Functions ◽  
Weighted Norm Inequality ◽  
Weighted Norm ◽  
Hankel Transformation ◽  
Negative Weight ◽  
Boundedness Theorem ◽  
Image Position

SynopsisWe give conditions on pairs of non-negative weight functions U and V which are sufficient that for 1<p≤<∞where Hλ is the Hankel transformation.The technique of proof is a variant of Muckenhoupt's recent proof for the boundedness of the Fourier transformation between weighted Lp spaces, and we can also use this variant to prove a somewhat different boundedness theorem for the Fourier transformation.

Weighted norm inequalities of sum form involving derivatives

1981 ◽  
Vol 88 (1-2) ◽  
pp. 121-134 ◽  
Author(s):  
Man Kam Kwong ◽  
A. Zettl
Keyword(s):  
Weight Functions ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Negative Weight ◽  
Image Position ◽  
Unbounded Intervals ◽  
General Conditions

SynopsisHere we obtain the inequalityunder very general conditions on the non-negative weight functions u, v, w, for general p, l≦p<∞ and for both bounded and unbounded intervals I.

Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel

1998 ◽  
Vol 50 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Rough Kernel ◽  
Degree Zero ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
Image Position

AbstractGiven function Ω on ℝn , we define the fractional maximal operator and the fractional integral operator by and respectively, where 0 < α < n. In this paper we study the weighted norm inequalities of MΩα and TΩα for appropriate α, s and A(p, q) weights in the case that Ω∈ Ls(Sn-1)(s> 1), homogeneous of degree zero.

Function Spaces

1953 ◽  
Vol 5 ◽  
pp. 273-288 ◽  
Author(s):  
Israel Halperin
Keyword(s):  
Banach Spaces ◽  
Measure Space ◽  
Function Spaces ◽  
Weight Functions ◽  
Negative Weight ◽  
Image Position

This paper is the first in a series dealing with Banach spaces L whose elements are functions on a measure space S. If W is a family of non-negative weight functions wα we sometimes write LWp when the norm is given as

scholarly journals Weighted norm inequalities for multilinear singular integral operators and applications

2014 ◽  
Vol 12 (03) ◽  
pp. 269-291 ◽  
Author(s):  
Guoen Hu ◽  
Chin-Cheng Lin
Keyword(s):  
Singular Integral ◽  
Fourier Multiplier ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Weighted Estimate ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Weighted Estimates ◽  
Multilinear Singular Integral

In this paper, weighted norm inequalities with Ap weights are established for the multilinear singular integral operators whose kernels satisfy certain Lr′-Hörmander regularity condition. As applications, we recover a weighted estimate for the multilinear Fourier multiplier obtained by Fujita and Tomita, and obtain several new weighted estimates for the multilinear Fourier multiplier as well.

Weighted Restriction for Curves

1993 ◽  
Vol 36 (1) ◽  
pp. 87-95 ◽  
Author(s):  
Joseph D. Lakey
Keyword(s):  
Fourier Transform ◽  
Weight Function ◽  
Weighted Norm ◽  
Two Dimensional ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Restriction Theorems ◽  
Nonnegative Weight ◽  
The Fourier Transform ◽  
Image Position

AbstractWe prove weighted norm inequalities for the Fourier transform of the formwhere v is a nonnegative weight function on ℝd and ψ: [— 1,1 ] —> ℝd is a nondegenerate curve. Our results generalize unweighted (i.e. v = 1) restriction theorems of M. Christ, and two-dimensional weighted restriction theorems of C. Carton-Lebrun and H. Heinig.

On the Boundedness and Range of the Extended Hankel Transformation

1980 ◽  
Vol 23 (3) ◽  
pp. 321-325 ◽  
Author(s):  
P. G. Rooney
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Hankel Transformation ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Compactly Supported ◽  
Image Position

For l≤p<∞ μ∈ℝ, let ℒμ.p denote the collection of functions f, measurable on (0, ∞) and such thatLet C0 be the collection of functions continuous and compactly supported on (0, ∞); it is known that C0 is dense in ℒμ.p—see [2; Lemma 2.2]. If X and Y are Banach spaces, denote by [X, Y] the collection of bounded linear operators from X into Y, abbreviating [X, X] to [X].

Weighted norm inequalities involving gradients

1989 ◽  
Vol 112 (3-4) ◽  
pp. 331-341 ◽  
Author(s):  
C. Carton-Lebrun ◽  
H. P. Heinig
Keyword(s):  
Weight Functions ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Large Classes

SynopsisLet then, for certain weight functions u and v and indices p,q, it is shown that ∥Tαf∥q, u≦C∥grad f ∥p, v'q > n / α holds. For α=l,p=q and u = v ≡ l this reduces to a result of M. Weiss. In addition we establish n-dimensional weighted Hardy—Littlewood type inequalities ofthe form for large classes of weights.

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