This paper discusses the convexity of range Berezin transform. For a bounded operator T acting on reproducing kernel Hilbert space H (on set X), this is B(T):={?Tkˆx,kˆx?H:x?X}, where kˆx normalized for at x?X. Primarily, we focus characterizing class composition operators Hardy unit disk.

In this paper, we obtain the weighted boundedness for local multi(sub)linear Hardy–Littlewood maximal operators and multilinear fractional integral associated with Muckenhoupt weights on Gaussian measure spaces. We deal these problems by introducing a new pointwise equivalent “radial” definitions of operators. Moreover, using similar approach, also get rough kernel

In this paper, we introduce the p-adic Hardy type operator and obtain its sharp bound on the p-adic Lebesgue product spaces. Meanwhile, an analogous result is computed for the p-adic Lebesgue product spaces with power weights. In addition, we characterize a sufficient and necessary condition which ensures that the weighted p-adic Hardy type operator is bounded on the p-adic Lebesgue product spa...

Abstract In this paper, we completely characterize the boundedness and compactness of Volterra integration operators $J_{g}$ J g acting from Hardy-type tent spaces HT q , α </mm...

In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.

We established some new α-conformable dynamic inequalities of Hardy–Knopp type. Some generalizations Hardy type in two variables on time scales are established. Furthermore, we investigated Hardy’s inequality for several functions calculus. Our results proved by using two-dimensional Jensen’s and Fubini’s theorem scales. When α=1, then obtain well-known time-scale due to Hardy. As special cases...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

Given a non-increasing and radially symmetric kernel in $$L ^ 1 _{\textrm{loc}} (\mathbb {R}^ 2 ; \mathbb {R}_+)$$ , we investigate counterparts of the classical Hardy–Littlewood Riesz inequalities when class admissible domains is family polygons with given area N sides. The latter corresponds to study polygonal isoperimetric problem nonlocal version. We prove that, for every $$N \ge 3$$ regula...

We consider Hardy operators on the half-space, that is, ordinary and fractional Schrödinger with potentials given by appropriate power of distance to boundary. show scales homogeneous Sobolev spaces generated Laplacian are comparable each other when coupling constant is not too large in a quantitative sense. Our results extend those whole Euclidean space rely recent heat kernel bounds.