Results 41 to 50 of about 3,261,817 (215)

Characterization of Riesz and Bessel potentials on variable Lebesgue spaces

Journal of Function Spaces and Applications, 2006
Riesz and Bessel potential spaces are studied within the framework of the Lebesgue spaces with variable exponent. It is shown that the spaces of these potentials can be characterized in terms of convergence of hypersingular integrals, if one assumes that
Alexandre Almeida, Stefan Samko
doaj   +1 more source

Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces

Journal of Function Spaces, 2019
In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·)
Xukui Shao, Shuangping Tao
doaj   +1 more source

Forecasting Duration in High‐Frequency Financial Data Using a Self‐Exciting Flexible Residual Point Process

Journal of Forecasting, EarlyView.
ABSTRACT This paper presents a method for forecasting limit order book durations using a self‐exciting flexible residual point process. High‐frequency events in modern exchanges exhibit heavy‐tailed interarrival times, posing a significant challenge for accurate prediction.
Kyungsub Lee
wiley   +1 more source

Fractional Sobolev spaces with variable exponents and fractional $p(x)$-Laplacians

Electronic Journal of Qualitative Theory of Differential Equations, 2017
In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces.
Uriel Kaufmann, Julio Rossi, Raul Vidal
doaj   +1 more source

Existence and Uniqueness of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and L1-Data

International Journal of Differential Equations, 2023
Nonlinear partial differential equations are considered as an essential tool for describing the behavior of many natural phenomena. The modeling of some phenomena requires to work in Sobolev spaces with constant exponent.
Ibrahime Konaté, Arouna Ouédraogo
doaj   +1 more source

Kernel Bounds for Parabolic Operators Having First‐Order Degeneracy at the Boundary

Mathematische Nachrichten, EarlyView.
ABSTRACT We study kernel estimates for parabolic problems governed by singular elliptic operators ∑i,j=1N+1qijDij+cDyy,cγ+1>0,γ=qN+1,N+1,$$\begin{equation*} \sum _{i,j=1}^{N+1}q_{ij}D_{ij}+c\frac{D_y}{y},\qquad \frac{c}{\gamma }+1>0, \quad \gamma =q_{N+1,N+1}, \end{equation*}$$in the half‐space R+N+1={(x,y):x∈RN,y>0}$\mathbb {R}^{N+1}_+=\lbrace (x,y ...
L. Negro, C. Spina
wiley   +1 more source

Linear functionals on variable exponent Bochner–Lebesgue spaces

Rendiconti Lincei, Matematica e Applicazioni, 2019
We characterize the linear functionals on variable exponent Bochner–Lebesgue spaces in terms of the variable exponent Riesz bounded variation spaces for vector measures, which are introduced in this paper.
Castillo, René Erlín, Guzmán, Oscar M., Rafeiro, Humberto   +2 more
openaire   +1 more source

Grothendieck and ℓ∞$\ell _\infty$‐Grothendieck Subspaces of ℓ∞$\ell _\infty$

Mathematische Nachrichten, EarlyView.
ABSTRACT Let c=2ℵ0$\mathfrak {c}=2^{\aleph _0}$. We prove that ℓ∞$\ell _\infty$ contains 2c$2^{\mathfrak {c}}$ pairwise non‐isomorphic non‐reflexive Grothendieck subspaces. They may all be chosen to contain the canonical copy of c0$c_0$ and to have an infinite‐dimensional reflexive quotient. This is optimal and answers Problem 24 of González and Kania [
Manuel González, Tomasz Kania
wiley   +1 more source

Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces

Journal of Function Spaces, 2020
This paper is devoted to the maximal regularity of sectorial operators in Lebesgue spaces Lp⋅ with a variable exponent. By extending the boundedness of singular integral operators in variable Lebesgue spaces from scalar type to abstract-valued type, the ...
Qinghua Zhang, Yueping Zhu, Feng Wang
doaj   +1 more source

Cauchy problem for hyperbolic equations of third order with variable exponent of nonlinearity

Karpatsʹkì Matematičnì Publìkacìï, 2020
We investigate weak solutions of the Cauchy problem for the third order hyperbolic equations with variable exponent of the nonlinearity. The problem is considered in some classes of functions namely in Lebesgue spaces with variable exponents.
O.M. Buhrii, O.T. Kholyavka, P.Ya. Pukach, M.I. Vovk   +3 more
doaj   +1 more source