Interior Schauder-Type Estimates for Higher-Order Elliptic Operators in Grand-Sobolev Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2021 In this paper an elliptic operator of the $m$-th order $L$ with continuous coefficients in the $n$-dimensional domain $\Omega \subset R^{n} $ in the non-standard Grand-Sobolev space $W_{q)}^{m} \left(\Omega \right)\, $ generated by the norm $\left\| \,
Bilal Bilalov, Sabina Sadigova
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Approximation by matrix transform in generalized grand Lebesgue spaces with variable exponent
Journal of Numerical Analysis and Approximation Theory, 2021 In this work the Lipschitz subclass of the generalized grand Lebesgue space with variable exponent is defined and the error of approximation by matrix transforms in this subclass is estimated.
Ahmet Testici, Daniyal Israfilov
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Journal of Function Spaces, 2022 Let θ≥0 and p· be a variable exponent, and we introduce a new class of function spaces Lp·,θ in a probabilistic setting which unifies and generalizes the variable Lebesgue spaces with θ=0 and grand Lebesgue spaces with p·≡p and θ=1.
Libo Li, Zhiwei Hao
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Boundedness of Riesz Potential Operator on Grand Herz-Morrey Spaces
Axioms, 2022 In this paper, we introduce grand Herz–Morrey spaces with variable exponent and prove the boundedness of Riesz potential operators in these spaces.
Babar Sultan +4 more
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Boundedness of Multilinear Calderón-Zygmund Operators on Grand Variable Herz Spaces
Journal of Function Spaces, 2022 In this paper, we prove the boundedness of multilinear Calderón-Zygmund operators on product of grand variable Herz spaces. These results generalize the boundedness of multilinear Calderón-Zygmund operators on product of variable exponent Lebesgue spaces
Hammad Nafis +2 more
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Boundedness of some operators on grand Herz spaces with variable exponent
AIMS Mathematics, 2023 Our aim in this paper is to prove boundedness of an intrinsic square function and higher order commutators of fractional integrals on grand Herz spaces with variable exponent $ {\dot{K} ^{a(\cdot), u), \theta}_{ s(\cdot)}(\mathbb{R}^n)} $ by applying ...
Mehvish Sultan +3 more
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A note on the boundedness of Hardy operators in grand Herz spaces with variable exponent
AIMS Mathematics, 2023 The fractional Hardy-type operators of variable order is shown to be bounded from the grand Herz spaces $ {\dot{K} ^{a(\cdot), u), \theta}_{ p(\cdot)}(\mathbb{R}^n)} $ with variable exponent into the weighted space $ {\dot{K} ^{a(\cdot), u), \theta}_ ...
Samia Bashir +4 more
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Boundedness of Marcinkiewicz integral operator of variable order in grand Herz-Morrey spaces
AIMS Mathematics, 2023 Let $ \mathbb{S}^{n-1} $ denotes the unit sphere in $ \mathbb{R}^n $ equipped with the normalized Lebesgue measure. Let $ \Phi \in L^r(\mathbb{S}^{n-1}) $ be a homogeneous function of degree zero.
Mehvish Sultan +3 more
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Besov's Type Embedding Theorem for Bilateral Grand Lebesgue Spaces [PDF]
, 2010 In this paper we obtain the non-asymptotic norm estimations of Besov's type between the norms of a functions in different Bilateral Grand Lebesgue spaces (BGLS).
Ostrovsky, E., Sirota, L.
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Generalized Grand Lebesgue Spaces Associated to Banach Function spaces [PDF]
Sahand Communications in Mathematical AnalysisIn this paper we introduce the class of grand Lebesgue spaces associated to a Banach function space $X$ by replacing the role of the $L^1$-norm by the norm $\|\cdot\|_X$ in the classical construction of the generalized grand Lebesgue spaces.
Alireza Bagheri Salec +2 more
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