Let Q be a homogeneous function of degree zero that enjoys the vanishing condition on the unit sphere Sn-1(n >= 2). Let TQ be the convolution singular integral operator with kernel Q(x)|x|-n. In this paper, when Q ...
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Let Q be a homogeneous function of degree zero that enjoys the vanishing condition on the unit sphere Sn-1(n >= 2). Let TQ be the convolution singular integral operator with kernel Q(x)|x|-n. In this paper, when Q E L Co ( S n- 1 ), we consider quantitative weighted bounds of composite operators of TQ on rearrangement invariant Banach function spaces. These spaces contain classical Lorentz spaces and Orlicz spaces as special examples. Weighted boundedness of the composite operators on rearrangement invariant quasi-Banach spaces are also given.
For 1 < p < infinity, we show that the Rosenthal X p,w spaces and the Bourgain-Rosenthal-Schechtman R p omega space have the factorization property and the primary factorization property. (c) 2024 The Authors. P...
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For 1 < p < infinity, we show that the Rosenthal X p,w spaces and the Bourgain-Rosenthal-Schechtman R p omega space have the factorization property and the primary factorization property. (c) 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// ***/licenses/by/4.0/).
In this paper, we introduce and study the concept of p-height orthogonality in real normed linear spaces. This orthogonality generalizes the well-known Singer and height orthogonalities. First, we investigate main pro...
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In this paper, we introduce and study the concept of p-height orthogonality in real normed linear spaces. This orthogonality generalizes the well-known Singer and height orthogonalities. First, we investigate main properties of this type of orthogonality. Then, variety of examples are presented to illustrate the relationship between p-height orthogonality and other previously defined (e.g., isosceles, Singer, height and Birkhoff-James) orthogonalities. Also we investigate the existence properties of this new notion of orthogonality. In particular, alpha-existence property is established and some interesting bounds for the values of alpha are obtained. Moreover, some characterizations of inner product spaces are given in terms of p-height orthogonality and its relation with Pythagorean and Birkhoff-James orthogonalities. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data
This two-part work presents a novel theory for model reference adaptive control (MRAC) of deterministic nonlinear ordinary differential equations (ODEs) that contain functional, nonparametric uncertainties that reside...
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This two-part work presents a novel theory for model reference adaptive control (MRAC) of deterministic nonlinear ordinary differential equations (ODEs) that contain functional, nonparametric uncertainties that reside in a native space. The approach is unique in that it relies on interpreting the closed-loop control problem for the ODE as a simple type of distributed parameter system (DPS), from which implementable controllers are subsequently derived. A thorough comparative analysis between the proposed framework and classical MRAC is performed. The limiting distributed parameter system, which underlies the proposed adaptive control framework, is derived and discussed in detail in this first part of the paper. The second part of this work will detail numerous finite-dimensional implementations of the proposed native space-based approach.
We investigate here the density of the set of the restrictions from C-C(infinity)(R-d) to C-C(infinity)(Omega) in the Musielak-Orlicz-Sobolev space W-1,W-Phi(Omega). It is a continuation of article [15], where we have...
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We investigate here the density of the set of the restrictions from C-C(infinity)(R-d) to C-C(infinity)(Omega) in the Musielak-Orlicz-Sobolev space W-1,W-Phi(Omega). It is a continuation of article [15], where we have studied density of CC infinity(Rd) in W-k,W-Phi(R-d) for k is an element of N. The main theorem states that for an open subset Omega subset of R-d with its boundary of class C-1, and Musielak-Orlicz function Phi satisfying condition (A1) which is a sort of log-H & ouml;lder continuity and the growth condition Delta 2, the set of restrictions of functions from C-C(infinity)(R-d) to Omega is dense in W-1,W-Phi(Omega). We obtain a corresponding result in variable exponent Sobolev space W-1,W-p(& sdot;)(Omega) under the assumption that the exponent p(x) is essentially bounded on Omega and Phi(x,t)=t(p(x)), t >= 0, x is an element of Omega, satisfies the log-H & ouml;lder condition. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The initial-boundary value problem for the Schrodinger equation with cubic nonlinearities of the form u(3-k)u(k) is studied on the half-line. Using the Fokas solution formula for the corresponding linear forced proble...
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The initial-boundary value problem for the Schrodinger equation with cubic nonlinearities of the form u(3-k)u(k) is studied on the half-line. Using the Fokas solution formula for the corresponding linear forced problem linear estimates are derived with data in Sobolev spaces and forcing in Bourgain solution spaces. Then, using these linear estimates and the trilinear estimates indicated by the forcing it is shown that the iteration map defined by the Fokas solution formula is a contraction in appropriate solution spaces. Thus, local well-posedness is proved for Sobolev exponents s >= 0 when k = 0, 1, 2, and for s > -1/3 when k = 3. The methodology used is analogous to the one used for the corresponding initial value problems that is based on the Fourier transform for solving the forced linear problem. (c) 2024 Elsevier Inc. All rights reserved.
The purpose of this work is to show the iterate property for globally elliptic differential operators with polynomial coefficients (called Shubin operators), in the anisotropic Roumieu Gelfand-Shilov spaces S {M } { N...
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The purpose of this work is to show the iterate property for globally elliptic differential operators with polynomial coefficients (called Shubin operators), in the anisotropic Roumieu Gelfand-Shilov spaces S {M } { N} ( R n ). As a consequence we obtain a result of regularity of solutions of differential equations in these spaces. (c) 2024 Elsevier Masson SAS. All rights reserved.
A Banach space is said to have the Lebesgue property if every Riemann-integrable function f : [0 , 1] -> X is Lebesgue almost everywhere continuous. We give a characterization of the Lebesgue property in terms of a...
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A Banach space is said to have the Lebesgue property if every Riemann-integrable function f : [0 , 1] -> X is Lebesgue almost everywhere continuous. We give a characterization of the Lebesgue property in terms of a new sequential asymptotic structure that is strictly between the notions of spreading and asymptotic models. We also reproduce an apparently lost theorem of Pelczynski and da Rocha Filho that a subspace X subset of L 1 [0 , 1] has the Lebesgue property if every spreading model of X is equivalent to the unit vector basis of pound 1 . (c) 2024 Elsevier Inc. All rights reserved.
For any educational programme to be successful, it is essential to have a well-planned and comprehensive syllabus that fosters inclusivity and positive motivation. In my paper, I am going to examine the BA syllabi fro...
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The concept of meso news-spaces refers to online spaces located between the private and public realms, where everyday users, more professional media actors, or both, can produce and share news-related content among ea...
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The concept of meso news-spaces refers to online spaces located between the private and public realms, where everyday users, more professional media actors, or both, can produce and share news-related content among each other, yet not to a wide audience. Such spaces are afforded by digital media platforms, including, but not limited to, Facebook groups, X spaces, and group chats on WeChat, WhatsApp, or Telegram. This special issue is devoted to further understanding news-related communication that occurs neither in fully public nor fully private realms, but between or across the two. In the introduction to the special issue, we demonstrate the significance of meso news-spaces by considering the example of the use of WhatsApp groups in the mobilization of the pro-democracy movement in Israel in 2023. We then consider the challenges that meso news-spaces pose for researchers, in terms of conceptualization, research ethics, and context. We conclude with a review of the articles of the special issue, and with directions for future research around this phenomenon, that is proving to be a significant one in the digital news environment.
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