Uniqueness and normality for M. riesz potentials and solutions of the darboux equation

1998 ◽  
Vol 92 (1) ◽  
pp. 3635-3639
Author(s):  
A. I. Sergeev
Keyword(s):  
Riesz Potentials ◽  
Darboux Equation

scholarly journals B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials on B-Morrey spaces

2020 ◽  
Vol 18 (1) ◽  
pp. 715-730
Author(s):  
Javanshir J. Hasanov ◽  
Rabil Ayazoglu ◽  
Simten Bayrakci
Keyword(s):  
Differential Operator ◽  
Singular Integral ◽  
Riesz Potential ◽  
Type Theorem ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Sobolev Type ◽  
Riesz Potentials ◽  
Bessel Differential Operator

Abstract In this article, we consider the Laplace-Bessel differential operator {\Delta }_{{B}_{k,n}}=\mathop{\sum }\limits_{i=1}^{k}\left(\frac{{\partial }^{2}}{\partial {x}_{i}^{2}}+\frac{{\gamma }_{i}}{{x}_{i}}\frac{\partial }{\partial {x}_{i}}\right)+\mathop{\sum }\limits_{i=k+1}^{n}\frac{{\partial }^{2}}{\partial {x}_{i}^{2}},{\gamma }_{1}\gt 0,\ldots ,{\gamma }_{k}\gt 0. Furthermore, we define B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials associated with the Laplace-Bessel differential operator. Moreover, we also obtain the boundedness of the B-maximal commutator {M}_{b,\gamma } and the commutator {[}b,{A}_{\gamma }] of the B-singular integral operator and Hardy-Littlewood-Sobolev-type theorem for the commutator {[}b,{I}_{\alpha ,\gamma }] of the B-Riesz potential on B-Morrey spaces {L}_{p,\lambda ,\gamma } , when b\in {\text{BMO}}_{\gamma } .

Boundedness of generalized Riesz potentials on commutative hypergroups

2015 ◽  
Vol 10 ◽  
pp. 333-338
Author(s):  
Mubariz G. Hajibayov
Keyword(s):  
Riesz Potentials

scholarly journals A trace inequality for generalized potentials in Lebesgue spaces with variable exponent

2004 ◽  
Vol 2 (1) ◽  
pp. 55-69 ◽  
Author(s):  
David E. Edmunds ◽  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Variable Exponent ◽  
Homogeneous Type ◽  
Trace Inequality ◽  
Spaces Of Homogeneous Type ◽  
Weighted Inequality ◽  
Euclidean Spaces ◽  
Riesz Potentials ◽  
Lebesgue Spaces ◽  
Fractal Sets

A trace inequality for the generalized Riesz potentialsIα(x)is established in spacesLp(x)defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces. As a corollary a criterion for a two-weighted inequality in classical Lebesgue spaces for potentialsIα(x)defined on fractal sets is derived.

On the Euler-Poisson-Darboux equation

1970 ◽  
Vol 23 (1) ◽  
pp. 89-102 ◽  
Author(s):  
A. Erdélyi
Keyword(s):  
Darboux Equation

scholarly journals On the uncertainty principle for M. Riesz potentials

2001 ◽  
Vol 39 (2) ◽  
pp. 223-243
Author(s):  
Dmitri B. Beliaev ◽  
Victor P. Havin
Keyword(s):  
Uncertainty Principle ◽  
Riesz Potentials

scholarly journals Zero Sets of Solutions of the Generalized Darboux Equation

2017 ◽  
Vol 2 (4) ◽  
pp. 272-280
Author(s):  
Valery Volchkov ◽  
◽  
Vitaly Volchkov ◽  
Keyword(s):  
Zero Sets ◽  
Darboux Equation
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