In this paper we establish a mean value property for the functions which is satisfied to Laplace–Bessel equation. Our results involve generalized divergence theorem and second Green’s identities relating bulk with boundary of region on differential Bessel operators act. Also design fractional weighted operator, study its boundedness, obtain maximal inequality spherical get boundedness. The conn...

The paper contains the inversion formula for weighted spherical mean. interest to reconstruction a function by its integral sphere grews tremendously in last six decades, stimulated spectrum of new problems and methods image reconstruction. We consider generalization classical mean inverse case when generalized translation acts instead regular. As particular this problem includes action means o...

A new reconstruction method is given for the spherical mean transform with centers on a plane in R which is also called Sonar transform. Standard inversion formulas require data over all spheres, but typically, the data are limited in the sense that the centers and radii are in a compact set. Our reconstruction operator is local because, to reconstruct at x, one needs only spheres that pass nea...

The linear Weingarten condition with ellipticity for the mean curvature and extrinsic Gaussian on a surface in three-sphere can define Riemannian metric which is called elliptic metric. We established some local characterizations of round spheres tori immersed 3-dimensional unit sphere, along Laplace operator, spherical Gauss map associated