본문 바로가기
KERD
논문KCI 등재

CHARACTERIZATION OF THE MULTIPLIERS FROM H r TO H −r

Sadek Gala|Yoshihiro Sawano
대한수학회 (The Korean Mathematical Society)|2013.05|대한수학회보 (Bulletin of the KMS)|제50권 제3호|pp. 915-928

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

Sobolev spacemultiplier spacefractional differentiation
주제분류수학

초록

In this paper, we will provide an alternative proof to char- acterize the pointwise multipliers which maps a Sobolev space . H r (Rd) to its dual . H −r (Rd) in the case 0 < r < d 2 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.

Abstract

In this paper, we will provide an alternative proof to char- acterize the pointwise multipliers which maps a Sobolev space . H r (Rd) to its dual . H −r (Rd) in the case 0 < r < d 2 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.

참고문헌 (15)

  1. S. Y. A. Chang, "Some weighted norm inequalities concerning the Schrodinger operators", Comment. Math. Helv, 60(2), pp.217~246 (1985)
  2. L. I. Hedberg, "On certain convolution inequalities", Proc. Amer. Math. Soc, 36, pp.505~510 (1972)
  3. R. Kerman, "The trace inequality and eigenvalue estimate for Schrodinger operators", Ann. Inst. Fourier, 36(4), pp.207~228 (1986)
  4. P. G. Lemari´e-Rieusset, "Multipliers between Sobolev spaces and fractional differentiation", J. Math. Anal. Appl, 322(2), pp.1030~1054 (2006)
  5. V. G. Mazya, "Sobolev Spaces" (1985), Springer-Verlag
  6. V. G. Mazya, "Theory of Multipliers in Spaces of Differentiable Functions" (1985), Pitnam
  7. V. G. Mazya, "Capacitary inequalities for fractional integrals with applications to partial differential equations and Sobolev multipliers", Ark. Mat, 33(1), pp.81~115 (1995)
  8. V. G. Mazya, "The Schrodinger operator on the energy space: boundedness and compactness criteria", Acta Math, 188(2), pp.263~302 (2002)
  9. V. G. Mazya, "The form boundedness criterion for the relativistic Schrodinger operator", Ann. Inst. Fourier, 54(2), pp.317~339 (2004)
  10. T. Miyakawa, "On L1-stability of stationary Navier-Stokes flows in Rn", J. Math. Sci. Univ. Tokyo, 4(1), pp.67~119 (1997)
  11. M. Schechter, "The spectrum of the Schrodinger operator", Trans. Amer. Math. Soc, 312(1), pp.115~128 (1989)
  12. E. M. Stein, "Singular Integrals and Differentiability Properties of Functions" (1970), Princeton Univ. Press
  13. E. M. Stein, "The characterization of functions arising as potentials", Bull. Amer. Math. Soc, 67, pp.102~104 (1961)
  14. E. M. Stein, "Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals" (1993), Princeton Univ. Press
  15. R. S. Strichartz, "Multipliers on fractional Sobolev spaces", J. Math. Mech, 16, pp.1031~1060 (1967)

관련 논문AI추천

CONTINUOUS CHARACTERIZATION OF THE TRIEBEL-LIZORKIN SPACES AND FOURIER MULTIPLIERS조영금대한수학회 · 대한수학회보2010 · 제47권 제4호Boundedness for fractional Hardy-type operator on Herz-Morrey spaces with variable exponentWU Jianglong대한수학회 · 대한수학회보2014 · 제51권 제2호WEAK FACTORIZATIONS OF H1(Rn) IN TERMS OF MULTILINEAR FRACTIONAL INTEGRAL OPERATOR ON VARIABLE LEBESGUE SPACESHuan Zhao, Zongguang Liu대한수학회 · 대한수학회보2023 · 제60권 제6호The boundedness of bilinear pseudodifferential operators in Triebel-Lizorkin and Besov spaces with variable exponentsLushun Wang, Yin Liu대한수학회 · 대한수학회보2024 · 제61권 제2호Lp-SOBOLEV REGULARITY FOR INTEGRAL OPERATORS OVER CERTAIN HYPERSURFACES양찬우, 허야용, 홍성금대한수학회 · 대한수학회보2014 · 제51권 제4호On the Boundedness of Marcinkiewicz Integrals on Variable Exponent Herz-type Hardy SpacesRabah Heraiz경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2019 · 제59권 제2호

이 간행물의 다른 논문 (29건)

A classification of half lightlike submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection이재원, 진대호pp. 705-717A note on LPI domainsKui Hu, Hanlin Chen, Fanggui Wangpp. 719-725Entropy and periodic orbits for generic diffeomorphismsRuixin Chenpp. 727-730Sets and value sharing of q-differences of meromorphic functionsXiao-Guang Qi, Lian-Zhong Yangpp. 731-745On discreteness of Mobius groupsXi Fupp. 747-752
원문 보기