A5011385857- Advanced Harmonic Analysis Research
- Differential Equations and Boundary Problems
- Spectral Theory in Mathematical Physics
- Numerical methods in inverse problems
- Advanced Mathematical Modeling in Engineering
- Holomorphic and Operator Theory
- Nonlinear Partial Differential Equations
- Mathematical Approximation and Integration
- Approximation Theory and Sequence Spaces
- Mathematical Analysis and Transform Methods
- Advanced Mathematical Physics Problems
- Probabilistic and Robust Engineering Design
- Advanced Banach Space Theory
- Mathematical functions and polynomials
- Electromagnetic Simulation and Numerical Methods
- Nonlinear Differential Equations Analysis
- Contact Mechanics and Variational Inequalities
- Matrix Theory and Algorithms
- Differential Equations and Numerical Methods
Kobe City College of Technology
2007-2020
Gakushuin University
1999-2000
The action of the generalized fractional integral operators and maximal is investigated in framework Morrey spaces. A typical property functions which belongs to spaces under pointwise multiplication by established. boundedness on predual shown as well. counterexample concerning Fefferman-Phong inequality given use characteristic function Cantor set.
In this paper, we study boundedness of integral operators on generalized Morrey spaces and its application to estimates in for the Schrödinger operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L 2 equals negative normal upper Delta plus V left-parenthesis x right-parenthesis W right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>=</mml:mo>...
In this paper we consider uniformly elliptic operators with non-negative potentials V on ℝn (n ≥ 3) which belong to certain reverse Hölder class. We show several estimates for VL–1, V1/2∇L–1 and ∇2L–1 weighted Lp spaces Morrey under assumptions aij(x), p. Our results generalize some of J. Zhong Z. Shen in the case L = –Δ + V(x) extend operators.
We show some inequalities for generalized fractional integral operators on Morrey spaces. also the boundedness property of predual
We consider the Schrödinger and type operators $H_{1}=-\Delta+V$ $H_2=(-\Delta)^2+V^2$ with non-negative potentials $V$ on $\mathbf{R}^n$. assume that potential belongs to reverse Hölder class which includes polynomials. establish estimates of fundamental solution for $H_{2}$ show some $L^p$ operators. Moreover, we operator $\nabla^4H_{2}^{-1}$ is a Calderón-Zygmund operator.
Boundedness of generalized fractional integral operators on Morrey spaces and their related results were shown by many authors.We consider one in a wider framework.Moreover, we show some inequalities for another operator integrals spaces.
We consider higher order Schrödinger type operators with nonnegative potentials. assume that the potential belongs to reverse Hölder class which includes polynomials. establish estimates of fundamental solution and show <svg style="vertical-align:-0.0pt;width:17.512501px;" id="M1" height="14.45" version="1.1" viewBox="0 0 17.512501 14.45" width="17.512501" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,14.387)"><path...
We study the magnetic Schrödinger operator $H$ on $R^n$, $n\geq3$. assume that electrical potential $V$ and {\bf a} belong to a certain reverse Hölder class, including case is non-negative polynomial components of are polynomials. show some estimates for operators type by using fundamental solution $H$. In particular, we $\nabla^2(-\Delta+V)^{-1}$ Calderón-Zygmund operator.
We consider higher order Schrödinger type operators with nonnegative potentials. assume that the potential belongs to reverse Hölder class which includes polynomials. show an operator of is a Calderón–Zygmund operator. also there exist potentials satisfy our assumptions but are not
In this paper we consider uniformly elliptic operators with non-negative potentials V on ℝn (n ≥ 3) which belong to certain reverse Hölder class. We show several estimates for VL–1, V1/2∇L–1 and ∇2L–1 weighted Lp spaces Morrey under assumptions aij(x), p. Our results generalize some of J. Zhong Z. Shen in the case L = –Δ + V(x) extend operators.
We consider higher order Schrödinger type operators with nonnegative potentials. assume that the potential belongs to reverse Hölder class which includes polynomials. establish estimates of fundamental solution and show Lp boundedness some operators. use pointwise by Hardy-Littlewood maximal operator prove our results.