$\require{mediawiki-texvc}$
  • 검색어에 아래의 연산자를 사용하시면 더 정확한 검색결과를 얻을 수 있습니다.
  • 검색연산자
검색연산자 기능 검색시 예
() 우선순위가 가장 높은 연산자 예1) (나노 (기계 | machine))
공백 두 개의 검색어(식)을 모두 포함하고 있는 문서 검색 예1) (나노 기계)
예2) 나노 장영실
| 두 개의 검색어(식) 중 하나 이상 포함하고 있는 문서 검색 예1) (줄기세포 | 면역)
예2) 줄기세포 | 장영실
! NOT 이후에 있는 검색어가 포함된 문서는 제외 예1) (황금 !백금)
예2) !image
* 검색어의 *란에 0개 이상의 임의의 문자가 포함된 문서 검색 예) semi*
"" 따옴표 내의 구문과 완전히 일치하는 문서만 검색 예) "Transform and Quantization"
쳇봇 이모티콘
안녕하세요!
ScienceON 챗봇입니다.
궁금한 것은 저에게 물어봐주세요.

논문 상세정보

BOUNDEDNESS OF MULTIPLE MARCINKIEWICZ INTEGRAL OPERATORS WITH ROUGH KERNELS

Abstract

This paper is concerned with giving some rather weak size conditions implying the $L^P$ boundedness of the multiple Marcin-kiewicz integrals for some fixed $1\;<\;p\;<\;{\infty}$, which essentially improve and extend some known results.

참고문헌 (26)

  1. A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85-139 
  2. J. Chen, Y. Ding, and D. Fan, $L^p$ boundedness of the rough Marcinkiewicz integral on product domains, Chinese J. Contemp. Math. 21 (2000), no. 1, 47-54 
  3. J. Chen, Y. Ding, and D. Fan, Certain square functions on product spaces, Math. Nachr. 230 (2001), 5-18 
  4. J. Chen, D. Fan, and Y. Ying, Rough Marcinkiewicz integrals with $L(log^+L)^2$ kernels on product spaces, Adv. Math. (China) 30 (2001), no. 2, 179-181 
  5. J. Chen, D. Fan, and Y. Ying, The method of rotation and Marcinkiewicz integrals on product domains, Studia Math. 153 (2002), no. 1, 41-58 
  6. S. Chanillo and R. L. Wheeden, Inequalities for Peano maximal functions and Marcinkiewicz integrals, Duke Math. J. 50 (1983), no. 3, 573-603 
  7. S. Chanillo and R. L. Wheeden, Relations between Peano derivatives and Marcinkiewicz integrals, in: Con- ference on harmonic analysis in honor of Antoni Zygmund, Vols. I, II (Chicago, Ill., 1981), 508-525, Wadsworth Math. Ser. Wadsworth, 1983 
  8. Y. Choi, Marcinkiewicz integrals with rough homogeneous kernels of degree zero in product domains, J. Math. Anal. Appl. 261 (2001), no. 1, 53-60 
  9. Y. Ding, $L^2$-boundedness of Marcinkiewicz integral with rough kernel, Hokkaido Math. J. 27 (1998), no. 1, 105-115 
  10. J. Duoandikoetxea, Multiple singular integrals and maximal functions along hypersurfaces, Ann. Inst. Fourier (Gronble) 36 (1986), no. 4, 185-206 
  11. R. Fefferman and E. M. Stein, Singular integrals on product spaces, Adv. Math. 45 (1982), no. 2, 117-143 
  12. L. Grafakos and A. Stefanov, $L^p$ bounds for singular integrals and maximal singular integrals with rough kernels, Indiana Univ. Math. J. 47 (1998), no. 2, 455-469 
  13. G. Hu, S. Lu, and D. Yan, $L^p(\mathbb{R}^m\;\times\;\mathbb{R}^n)$ boundedness for the Marcinkiewicz integral on product spaces, Sci. China Ser. A 46 (2003), no. 1, 75-82 
  14. L. Hormander, Estimates for translation invariant operators in $L^p$ spaces, Acta Math. 104 (1960), 93-140 
  15. M. Sakamoto and K. Yabuta, Boundedness of Marcinkiewicz functions, Studia Math. 135 (1999), no. 2, 103-142 
  16. S. Sato, Remarks on square functions in the Littlewood-Paley theory, Bull. Austral. Math. Soc. 58 (1998), no. 2, 199-211 
  17. E. M. Stein, On the function of Littlewood-Paley, Lusin and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958), 430-466 
  18. E. M. Stein, Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integral, Princeton Univ. Press, Princeton, NJ, 1993 
  19. E. M. Stein, Problems in harmonic analysis related to curvature and oscillatory integrals, Proc. Internat. Congr. Math., Berkeley (1986), 196-221 
  20. E. M. Stein, Some geometrical concepts arising in harmonic analysis, Geom. Funct. Anal. Special Vol. (2000), 434-453 
  21. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, No. 30, Princeton Univ. Press, Princeton, New Jersey, 1970 
  22. T. Walsh, On the function of Marcinkiewicz, Studia Math. 44 (1972), 203-217 
  23. H. Wu, On Marcinkiewicz integral operators with rough kernels, Integral Equations Operator Theory 52 (2005), no. 2, 285-298 
  24. H. Wu, $L^p$ bounds for Marcinkiewicz integrals associated to surfaces of revolution, J. Math. Anal. Appl. (to appear) 
  25. H. Wu, General Littlewood-Paley functions and singular integral operators on product spaces, Math. Nachr. 279 (2006), no. 4, 431-444 
  26. Y. Ying, Investigations on some operators with rough kernels in harmonic anal- ysis, Ph. D. Thesis (in Chinese), Zhejiang Univ., Hangzhou, 2002 

이 논문을 인용한 문헌 (0)

  1. 이 논문을 인용한 문헌 없음

원문보기

원문 PDF 다운로드

  • ScienceON :

원문 URL 링크

원문 PDF 파일 및 링크정보가 존재하지 않을 경우 KISTI DDS 시스템에서 제공하는 원문복사서비스를 사용할 수 있습니다. (원문복사서비스 안내 바로 가기)

상세조회 0건 원문조회 0건

DOI 인용 스타일