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CHARACTERIZATION OF THE MULTIPLIERS FROM Ḣr TO Ḣ-r
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 Title & Authors
CHARACTERIZATION OF THE MULTIPLIERS FROM Ḣr TO Ḣ-r
Gala, Sadek; Sawano, Yoshihiro;
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 Abstract
In this paper, we will provide an alternative proof to characterize the pointwise multipliers which maps a Sobolev space to its dual in the case 0 < < by a simple application of the definition of fractional Sobolev space. The proof relies on a method introduced by Maz'ya-Verbitsky [9] to prove the same result.
 Keywords
multiplier space;Sobolev space;fractional differentiation;
 Language
English
 Cited by
 References
1.
S. Y. A. Chang, J. M. Wilson, and T. H. Wolf, Some weighted norm inequalities conce${\mathbb{R}}^n$ing the Schrodinger operators, Comment. Math. Helv. 60 (1985), no. 2, 217-246. crossref(new window)

2.
L. I. Hedberg, On certain convolution inequalities, Proc. Amer. Math. Soc. 36 (1972), 505-510. crossref(new window)

3.
R. Kerman and E. T. Sawyer, The trace inequality and eigenvalue estimate for Schrodinger operators, Ann. Inst. Fourier (Grenoble) 36 (1986), no. 4, 207-228.

4.
P. G. Lemarie-Rieusset and S. Gala, Multipliers between Sobolev spaces and fractional differentiation, J. Math. Anal. Appl. 322 (2006), no. 2, 1030-1054. crossref(new window)

5.
V. G. Maz'ya, Sobolev Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1985.

6.
V. G. Maz'ya and T. Schaposnikova, Theory of Multipliers in Spaces of Differentiable Functions, Pitnam, 1985.

7.
V. G. Maz'ya and I. E. Verbitsky, Capacitary inequalities for fractional integrals with applications to partial differential equations and Sobolev multipliers, Ark. Mat. 33 (1995), no. 1, 81-115. crossref(new window)

8.
V. G. Maz'ya and I. E. Verbitsky, The Schrodinger operator on the energy space: boundedness and compactness criteria, Acta Math. 188 (2002), no. 2, 263-302. crossref(new window)

9.
V. G. Maz'ya and I. E. Verbitsky, The form boundedness criterion for the relativistic Schrodinger operator, Ann. Inst. Fourier (Grenoble) 54 (2004), no. 2, 317-339. crossref(new window)

10.
T. Miyakawa, On $L^1$-stability of stationary Navier-Stokes flows in ${\mathbb{R}}^n$, J. Math. Sci. Univ. Tokyo 4 (1997), no. 1, 67-119.

11.
M. Schechter, The spectrum of the Schrodinger operator, Trans. Amer. Math. Soc. 312 (1989), no. 1, 115-128.

12.
E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970.

13.
E. M. Stein, The characterization of functions arising as potentials, Bull. Amer. Math. Soc. 67 (1961), 102-104. crossref(new window)

14.
E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton, New Jersey, 1993.

15.
R. S. Strichartz, Multipliers on fractional Sobolev spaces, J. Math. Mech. 16 (1967), 1031-1060.