Boundedness of pseudo-differential operator associated with fractional Hankel transform

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
Akhilesh Prasad ◽  
V. Singh
Keyword(s):  
Differential Operator ◽  
Integral Operator ◽  
Integral Representation ◽  
Integral Operators ◽  
Hankel Transform ◽  
Pseudo Differential Operator ◽  
Fractional Hankel Transform ◽  
Boundedness Result

AbstractA pseudo-differential operator (p.d.o.) associated with the fractional Hankel transform involving the symbol a(x, ξ) is defined. An integral representation of p.d.o. and boundedness result of the composition of operators Δμr and A μ,α are obtained. A generalized integral operator A μ,aα corresponding to p.d.o. is also defined and the properties of the product of two generalized integral operators corresponding to p.d.o. are studied.

PSEUDO-DIFFERENTIAL OPERATORS INVOLVING HANKEL–CLIFFORD TRANSFORMATION

2012 ◽  
Vol 05 (03) ◽  
pp. 1250040 ◽  
Author(s):  
Akhilesh Prasad ◽  
V. K. Singh ◽  
M. M. Dixit
Keyword(s):  
Differential Operator ◽  
Integral Representation ◽  
Differential Operators ◽  
Norm Inequality ◽  
Sobolev Type ◽  
Continuous Linear ◽  
Pseudo Differential Operator ◽  
Pseudo Differential Operators ◽  
Hankel Convolution ◽  
Type Spaces

Pseudo-differential operator (p.d.o) associated with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined and the Zemanian-type spaces Hμ(I) and S(I) are introduced. It is shown that the p.d.o is continuous linear map of the space Hμ(I) and S(I) into itself. An integral representation of p.d.o h1, μ, a is obtained. Using the Hankel convolution it is shown that p.d.o h1, μ, a satisfies a certain [Formula: see text]-norm inequality. Properties of Sobolev-type space [Formula: see text] are studied.

scholarly journals A boundedness result for Marcinkiewicz integral operator

2020 ◽  
Vol 18 (1) ◽  
pp. 829-836
Author(s):  
Laith Hawawsheh ◽  
Mohammad Abudayah
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Integrability Condition ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Marcinkiewicz Integral ◽  
Radial Functions ◽  
New Space ◽  
Marcinkiewicz Integral Operator ◽  
Boundedness Result

Abstract We extend a boundedness result for Marcinkiewicz integral operator. We find a new space of radial functions for which this class of singular integral operators remains {L}^{p} -bounded when its kernel satisfies only the sole integrability condition.

Pseudo-differential operator involving generalized Hankel–Clifford transformation

2016 ◽  
Vol 09 (01) ◽  
pp. 1650016
Author(s):  
P. D. Pansare ◽  
B. B. Waphare
Keyword(s):  
Differential Operator ◽  
Integral Representation ◽  
Growth Condition ◽  
Differential Operators ◽  
Function Spaces ◽  
Continuous Linear ◽  
Pseudo Differential Operator ◽  
Type Function ◽  
Linear Map ◽  
Pseudo Differential Operators

Pseudo-differential operators (p.d.os) involving generalized Hankel–Clifford transformation associated with the symbol [Formula: see text] whose derivatives satisfy certain growth condition are defined and the Zemanian type function spaces [Formula: see text] and [Formula: see text] are introduced. It is shown that p.d.o’s are continuous linear map of the space [Formula: see text] and [Formula: see text] into itself. Also an Integral representation of p.d.o is obtained.

scholarly journals On Newp-Valent Meromorphic Function Involving Certain Differential and Integral Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Aabed Mohammed ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Meromorphic Function ◽  
Integral Operator ◽  
Sufficient Conditions ◽  
Integral Operators

We define new subclasses of meromorphicp-valent functions by using certain differential operator. Combining the differential operator and certain integral operator, we introduce a generalp-valent meromorphic function. Then we prove the sufficient conditions for the function in order to be in the new subclasses.

scholarly journals Rough Marcinkiewicz integral operators

2001 ◽  
Vol 27 (8) ◽  
pp. 495-503 ◽  
Author(s):  
Hussain Al-Qassem ◽  
Ahmad Al-Salman
Keyword(s):  
Integral Operator ◽  
Unit Sphere ◽  
Homogeneous Function ◽  
Integral Operators ◽  
Mean Value ◽  
Marcinkiewicz Integral ◽  
Degree Zero ◽  
Polynomial Mapping ◽  
Marcinkiewicz Integral Operator ◽  
Boundedness Result

We study the Marcinkiewicz integral operatorM𝒫f(x)=(∫−∞∞|∫|y|≤2tf(x−𝒫(y))(Ω(y)/|y|n−1)dy|2dt/22t)1/2, where𝒫is a polynomial mapping fromℝnintoℝdandΩis a homogeneous function of degree zero onℝnwith mean value zero over the unit sphereSn−1. We prove anLpboundedness result ofM𝒫for roughΩ.

Deriving the integral representation of a fractional Hankel transform from a fractional Fourier transform

1998 ◽  
Vol 23 (15) ◽  
pp. 1158 ◽  
Author(s):  
Li Yu ◽  
Yingyang Lu ◽  
Xiaoming Zeng ◽  
Meichun Huang ◽  
Mouzhi Chen ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Integral Representation ◽  
Fractional Fourier Transform ◽  
Hankel Transform ◽  
Fractional Hankel Transform

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

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