The main objective of this paper is to generalize the Barut-Girardello transform (BG-transform) in two different ways as a pair of Barut-Girardello type transforms (BG-type transforms). Certain differential operators ...
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The main objective of this paper is to generalize the Barut-Girardello transform (BG-transform) in two different ways as a pair of Barut-Girardello type transforms (BG-type transforms). Certain differential operators related to it are introduced and then continuity of the differential operators as well as both BG-type transforms on Zemanian type function spaces are discussed. Translation and convolution operators associated with BG-type transforms are introduced and obtained their estimates in Lebesgue space. Moreover, pseudo-differential operators involving BG-type transforms are defined and discussed their continuity on Zemanian type function spaces. At the end, some applications have been discussed.
The operation of extending functions from to is -continuous, so it is natural to study -continuous maps systematically if we want to find out which properties of "lift" to . We study the properties preserved...
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The operation of extending functions from to is -continuous, so it is natural to study -continuous maps systematically if we want to find out which properties of "lift" to . We study the properties preserved by -continuous maps and bijections both in general spaces and in . We show that -continuous maps preserve primary -property as well as countable compactness. On the other hand, existence of an -continuous injection of a space to a second countable space does not imply -diagonal in;however, existence of such an injection for a countably compact implies metrizability of . We also establish that -continuous injections can destroy caliber in pseudocompact spaces. In the context of relating the properties of and , a countably compact subspace of remains countably compact in the topology of;however, compactness, pseudocompactness, Lindelof property and Lindelof -property can be destroyed by strengthening the topology of to obtain the space . We show that Lindelof-property of together with being a caliber of implies that is cosmic.
We introduce generalized local and global Herz spaces where all their characteristics are variable. As one of the main results we show that variable Morrey type spaces and complementary variable Morrey type spaces are...
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We introduce generalized local and global Herz spaces where all their characteristics are variable. As one of the main results we show that variable Morrey type spaces and complementary variable Morrey type spaces are included into the scale of these generalized variable Herz spaces. We also prove the boundedness of a class of sublinear operators in generalized variable Herz spaces with application to variable Morrey type spaces and their complementary spaces, based on the mentioned inclusion.
Given a subset D of the Euclidean space, we study nonlocal quadratic forms that take into account tuples (x, y) is an element of D x D if and only if the line segment between x and y is contained in D. We discuss regu...
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Given a subset D of the Euclidean space, we study nonlocal quadratic forms that take into account tuples (x, y) is an element of D x D if and only if the line segment between x and y is contained in D. We discuss regularity of the corresponding Dirichlet form leading to the existence of a jump process with visibility constraint. Our main aim is to investigate corresponding Poincare inequalities and their scaling properties. For dumbbell shaped domains we show that the forms satisfy a Poincare inequality with diffusive scaling. This relates to the rate of convergence of eigenvalues in singularly perturbed domains.
We use Bochner's subordination technique to obtain caloric smoothing estimates in Besov- and Triebel-Lizorkin spaces. Our new estimates extend known smoothing results for the Gauss-Weierstrass, Cauchy-Poisson and ...
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We use Bochner's subordination technique to obtain caloric smoothing estimates in Besov- and Triebel-Lizorkin spaces. Our new estimates extend known smoothing results for the Gauss-Weierstrass, Cauchy-Poisson and higher-order generalized Gauss-Weierstrass semigroups. Extensions to other function spaces (homogeneous, hybrid) and more general semigroups are sketched.
The complex convexity of Musielak-Orlicz function spaces equipped with the p-Amemiya norm is mainly discussed. It is obtained that, for any Musielak-Orlicz function space equipped with the p-Amemiya norm when 1 <= ...
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The complex convexity of Musielak-Orlicz function spaces equipped with the p-Amemiya norm is mainly discussed. It is obtained that, for any Musielak-Orlicz function space equipped with the p-Amemiya norm when 1 <= p < infinity, complex strongly extreme points of the unit ball coincide with complex extreme points of the unit ball. Moreover, criteria for them in above spaces are given. Criteria for complex strict convexity and complex midpoint locally uniform convexity of above spaces are also deduced.
A cliquish function f : R -> R is internally cliquish if its set of discontinuity points is nowhere dense. A Baire 1 function f : R -> R is internally Baire 1 if its set of discontinuity points is nowhere dense....
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A cliquish function f : R -> R is internally cliquish if its set of discontinuity points is nowhere dense. A Baire 1 function f : R -> R is internally Baire 1 if its set of discontinuity points is nowhere dense. In this paper we proved that the set of Darboux internally cliquish (Baire 1) functions is dense and sigma-strongly porous in the family of Darboux cliquish (Baire 1) functions.
In this paper, a brief study is made on the Legendre function related to the Lebedev-Skalskaya transform (LSL-transform) pairs. Some preliminary useful results are obtained. The translation and convolution operators a...
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In this paper, a brief study is made on the Legendre function related to the Lebedev-Skalskaya transform (LSL-transform) pairs. Some preliminary useful results are obtained. The translation and convolution operators are introduced and obtained their estimates on Lebesgue space. Further, continuity mapping of LSL-transforms, the translation and convolution operators are discussed over the function spaces H-m,H-n and G(k,n). Moreover, pseudo-differential operators involving LSL-transforms are defined and studied their continuity property over the spaces H-m,H-n and G(k,n). An integral representation of pseudo-differential operators are also given.
In this paper, we introduce and study the two versions of Y-transform, which are adjoint to each other. Certain differential operators associated with Y-transforms are defined and we establish various operational rela...
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In this paper, we introduce and study the two versions of Y-transform, which are adjoint to each other. Certain differential operators associated with Y-transforms are defined and we establish various operational relations. The continuity mappings of Y-transforms on Zemanian type function spaces are discussed. We also define the pseudo-differential operators involving Y-transforms and deduce some estimates. The solution to the Cauchy problem for the pseudo-differential equation is obtained using the theory of Y-transform.
Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be proved in the most general possible s...
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Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be proved in the most general possible setting. Two important classes of fractional-calculus operators are the fractional integrals and derivatives with respect to functions (dating back to the 1970s) and those with general analytic kernels (introduced in 2019). To cover both of these settings in a single study, we can consider fractional integrals and derivatives with analytic kernels with respect to functions, which have never been studied in detail before. Here we establish the basic properties of these general operators, including series formulae, composition relations, function spaces, and Laplace transforms. The tools of convergent series, from fractional calculus with analytic kernels, and of operational calculus, from fractional calculus with respect to functions, are essential ingredients in the analysis of the general class that covers both.
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