In this paper, we compute several geometric constants for mixed Morrey spaces and mixed Morrey double-sequence spaces, specifically generalized Von Neumann-Jordan constant, modified Von Neumann-Jordan constants, and Zbáganu constant. For the calculation of these constants, we construct two functions of unit norm so that the upper bound of these constants is attained. In addition, we use an inequality involving these constants and Von Neumann-Jordan constant. Our results can be seen as some extensions of the previous results about geometric constants for Morrey spaces and discrete Morrey spaces.

In this paper, we investigate the boundedness of sublinear operators generated by fractional integrals as well as sublinear operators generated by Calderón-Zygmund operators on generalized weighted Morrey spaces and generalized weighted mixed-Morrey spaces. In particular, we are interested in the strong-type estimate for 1

We compute several geometric constants for mixed Morrey spaces, namely von Neumann-Jordan constant, James constant, and Dunkl-Williams constant. Through the values of the constants that we obtain, we know that mixed Morrey spaces are not uniformly convex nor uniformly nonsquare. Our result extends previous results on geometric constants for discrete Morrey spaces.

We construct a function which confirms the proper inclusion property of Morrey spaces, by using a relation between a class of functions, in Morrey spaces and discrete Morrey spaces. Our particular function is simpler than those constructed by H. Gunawan, D. I. Hakim, M. Idris (2018) and H. Gunawan, D. I. Hakim, M. Idris (2022).

In this article, we prove that mixed Morrey double-sequence spaces can be realized as a subspace of mixed Morrey spaces. Our proof extends a similar result for discrete Morrey spaces, obtained by Kikianty and Schwanke in 2019. As an application, we provide simple proofs of several inclusion results in mixed Morrey spaces and mixed Morrey double-sequence spaces.

In this paper, we shall discuss two formulae for the angle between two subspaces, or more generally the angle from a subspace of dimension $p$ to another subspace of dimension $q$ with $1\le p\le q\le \dim(X)$, in an inner product space $X$. In particular, we shall see that the two seemingly different formulae, one is obtained by H. Gunawan, O. Neswan, and W. Setya-Budhi in 2005 and the other by N. Wildberger in 2017, are actually identical.

The issue of the denseness property of smooth functions has been considered in many studies. To allow approximation by smooth functions in generalized Morrey spaces, generalized Zorko spaces and vanishing-type spaces are defined. While the generalized Zorko space employs the first-order difference, we construct a subspace of the generalized Morrey space utilizing the second-order difference. We investigate its properties concerning approximation by smooth functions and its relation to the generalized Zorko space.

In this paper, we present an embedding from discrete Morrey spaces to continuous Morrey Spaces which can be seen as a refinement of the result in [1]. We obtain the result by using a different norm on discrete Morrey spaces, which is equivalent to the existing norm.

In this paper, we study the relation between Stummel spaces, Morrey spaces, and Lebesgue spaces. We show the existence of embedding from Lebesgue spaces to Stummel spaces, and from Morrey spaces to Stummel spaces. The key of showing the existence of embeddings relies on the boundedness of Riesz potential operator both in Morrey spaces and Lebesgue spaces.

In this paper, we study relations between inner products derived from the standard n-inner product defined on an inner product space. In particular, we are interested in knowing when orthogonality with respect to the original inner product is preserved by the derived inner product.

In the continuous setting, Morrey spaces have been studied extensively, especially since the late 1960s. Meanwhile, Morrey sequence spaces, which are also known as discrete Morrey spaces, have only been developed by Gunawan et al. since 2018. In this article, we extend some known results on their inclusion properties and their (lack of) uniform nonsquareness to mixed Morrey double-sequence spaces, i.e. Morrey double-sequence spaces equipped with a mixed norm. As in the calculation of three geometric constants of Morrey spaces by Gunawan et al. in 2019, we also compute three geometric constants, namely Von Neumann-Jordan constant, James constant, and Dunkl-Williams constant for mixed Morrey double-sequence spaces. These constants measure uniformly nonsquareness of any Banach space. Through the values of the three constants, we reveal that mixed Morrey double-sequence spaces are not uniformly nonsquare. A relation between mixed Morrey double-sequence spaces and mixed Morrey spaces is also discussed.

Nakai's initial mathematical accomplishment centered on characterizing pointwise multipliers for functions with bounded mean oscillation (BMO).For the case in which BMO was defined on the torus T n , Stegenga and Janson had independently solved this characterization.However, in 1983, while pursuing a master's degree under the guidance of his supervisor Kôzô Yabuta, Nakai successfully provided a solution for the case in which BMO was defined on Euclidean space R n .This work was published in 1985.To obtain this characterization, he devised a function space defined by mean oscillation controlled by variable growth conditions.Nakai's subsequent research consistently revolved around function spaces L p,ϕ (R n ), generalized Campanato spaces, based on mean oscillation controlled by variable growth conditions.In 2005, his work on pointwise multipliers for BMO(R n ) was used by Lerner to study the class P(R n ) of functions p(•) for which the Hardy-Littlewood maximal operator is bounded on Lebesgue spaces L p(•) (R n ) with variable exponents.This work positively resolved a conjecture by Deining, which had suggested the existence of discontinuous functions within P(R n ).In 2012, Nakai and Yoshihiro Sawano discovered that the dual space of the Hardy space H p(•) (R n ) with variable exponents can be expressed as L p,ϕ (R n ).Furthermore, in 2019, Nakai and Tsuyoshi Yoneda utilized the function space L p,ϕ (R n ) to study the Navier-Stokes equations.Nakai also introduced generalized Morrey spaces with variable growth conditions and investigated the boundedness of integral operators on them.These results were presented in a paper in 1993, which has been cited in more than 250 papers to date.In 2000, Nakai studied a generalization of the Hardy-Littlewood-Sobolev theorem, which concerned the boundedness of fractional integral operators I α from L p (R n ) to L q (R n ).He extended this theorem to Orlicz spaces by introducing generalized fractional integral operators I ρ .He also extended the theorem to generalized Morrey-Campanato spaces in 2002.Moreover, in 2004, he introduced Orlicz-Morrey spaces and studied the boundedness of I ρ on them.After 2008, he started to research general-

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Muh Nur, Anna Islamiyati, Hendra Gunawan; g*-Angle between two subspaces in the space of p-summable sequences. AIP Conference Proceedings 25 January 2023; 2554 (1): 020002. https://doi.org/10.1063/5.0103813 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

In this paper we prove Fefferman's inequalities associated to potentials belonging to a generalized Morrey space or a Stummel class. We also show that the logarithm of a non-negative weak solution to a second order elliptic partial differential equation with potential in a generalized Morrey space or a Stummel class, under some assumptions, belongs to the bounded mean oscillation class. As a consequence, this elliptic partial differential equation has the strong unique continuation property. An example of an elliptic partial differential equation with potential in a Morrey space or a Stummel class which does not satisfy the strong unique continuation is presented.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Dahliatul Hasanah, Hendra Gunawan, Johan Matheus Tuwankotta; Functions in vanishing morrey spaces. AIP Conference Proceedings 23 January 2023; 2588 (1): 050001. https://doi.org/10.1063/5.0111736 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

Abstract We discuss a necessary condition for inclusion relations of weak type discrete Morrey spaces which can be seen as an extension of the results in [H. Gunawan, E. Kikianty and C. Schwanke, Discrete Morrey spaces and their inclusion properties, Math. Nachr. 291 2018, 8–9, 1283–1296] and [D. D. Haroske and L. Skrzypczak, Morrey sequence spaces: Pitt’s theorem and compact embeddings, Constr. Approx. 51 2020, 3, 505–535]. We also prove a proper inclusion from weak type discrete Morrey spaces into discrete Morrey spaces. In addition, we give a necessary condition for this inclusion. Some connections between the inclusion properties of discrete Morrey spaces and those of Morrey spaces are also discussed.

In this article, we compute Von-Neumann-Jordan constant, James constant, and Dunkl-Williams constant for small Morrey spaces. We find that the three constants are the same as those for the classical Morrey spaces.

Recently, we have seen the phenomena in use of partial differential equations (PDEs) especially in fluid dynamic area.The classical approach of the analysis of PDEs were dominated in early nineteenth century.As we know that for PDEs the fundamental theoretical question is whether the model problem consists of equation and its associated side condition is well-posed.There are many ways to investigate that the model problems are well-posed.Because of that reason, in this paper we consider the R-boundedness of the solution operator families for Navier-Lamé equation by taking into account the surface tension in a bounded domain of Ndimensional Euclidean space (N ≥ 2) as one way to study the well-posedess.We investigate the Rboundedness in half-space domain case.The R-boundedness implies not only the generation of analytic semigroup but also the maximal L p -L q regularity for the initial boundary value problem by using Weis's operator valued Fourier multiplier theorem for time dependent problem. it was known that the maximal L p -L q regularity class is the powerful tool to prove the well-posesness of the model problem.This result can be used for further research for example to analyze the boundedness of the solution operators of the model problem in bent-half space or general domain case.