Publication Cover
Applicable Analysis
An International Journal
Volume 45, 1992 - Issue 1-4
21
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Bessel potential operators for the quarter-plane

&
Pages 49-68 | Published online: 02 May 2007

References

  • Aronszajn , N. and Smith , K.T. 1961 . Theory of Bessel Potentials, Part 1 . Ann. de l'Inst. Fourier , 11 : 385 – 475 .
  • Calderón , A.P. 1961 . “ Lebesgue spaces of differentiable functions and distributions In: Partial Differential Equations ” . In Amer. Math. Soc , Edited by: Morrey , C.B. 33 – 49 . Providence .
  • Duduchava , R. 1979 . Integral Equations with Fixed Singularities , Leipzig : Teubner .
  • Duduchava , R. 1984 . On multidimensional singular integral operators. I: The half-space case . J. Operator Theory , 11 : 41 – 76 .
  • Duduchava , R. 1984 . On multidimensional singular integral operators. II: The case of compact manifolds . J. Operator Theory , 11 : 199 – 214 .
  • Duduchava , R. and Schneider , R. 1987 . The algebra of non-classical singular integral operators on half space . Int. Equ. Op. Theory , 10 : 531 – 553 .
  • Èskin , G.I. 1981 . “ Boundary Value Problems for Elliptic Pseudodifferential Equations ” . In AMS Transl. Math. Monogr , Vol. 52 , Providence .
  • Gelman , I.W. and Mazja , W.G. 1981 . Abschätzungen fur Differentialoperatoren im Halbraum , Berlin : Akademie-Verlag .
  • Hörmander , L. 1960 . Estimates for translation invariant operators in Lp spaces . Acta Math , 104 : 93 – 139 .
  • Hörmander , L. 1985 . The Analysis of Linear Partial Differential Operators III , Berlin : Springer .
  • Kraut , E.A. 1968 . Elastic-wave propagation and the factorization of matrix-valued functions of several complex variables . J. Math. Phys. , 9 : 1481 – 1487 .
  • Meister , E. and Speck , F.-O. 1987 . Scalar diffraction problems for Lipschitz and polygonal screens . Z. Ang. Math. Mech , 67 : T434 – 435 .
  • Meister , E. and Speck , F.-O. 1987 . “ Boundary integral equation methods for canon-ical problems in diffraction theory ” . In Boundary Elements IX , Edited by: Brebbia , C.A. , Wendland , W.L. and Kuhn , G. Vol. 1 , 59 – 77 . Berlin : Springer .
  • Meister , E. and Speck , F.-O. 1988 . A contribution to the quarter-plane problem in diffraction theory . J. Math. Anal. Appl. , 130 : 223 – 236 .
  • Peetre , J. 1961 . Another approach to elliptic boundary problems . Comm. Pure Appl. Math. , 14 : 711 – 731 .
  • Rabinovic , V.S. 1971 . Pseudodifferential equations in unbounded regions . Soviet Math. Dokl. , 12 : 452 – 456 .
  • Rabinovič , V.S. 1972 . Pseudodifferential operators on a class of noncompact manifolds . Math. USSR Sbornik , 18 : 45 – 59 .
  • Radlow , J. 1961 . Diffraction by a quarter-plane . Arch. Rat. Mech. Anal. , 8 : 139 – 158 .
  • Radlow , J. 1965 . Note on the diffraction at a corner . Arch. Rat. Mech. Anal. , 19 : 62 – 70 .
  • Sadosky , C. and Cotlar , M. 1967 . “ On quasi-homogeneous Bessel potential opera-tors, In: Singular Integrals ” . In Amer. Math. Soc , Edited by: Calderón , A.P. 275 – 287 . Providence .
  • R. Schneider, Contributions to the Theory of Elliptic Pseudodifferential Operators on Manifolds with Nonsmooth Boundaries, Ph.D. Thesis, Tech-nische Hochschule Darmstadt, 1989.
  • Schwartz , L. 1950 . Théorie des Distributions I, II , 51 – 51 . Paris : Hermann .
  • Shamir , E. 1966 . A remark on the Mikhlin-Hörmander multiplier theorem . J. Math. Anal. Appl. , 16 : 104 – 107 .
  • Shamir , E. 1967 . Elliptic systems of singular integral operators. I. The half-space case . Transact. Amer. Math. Soc. , 127 : 107 – 124 .
  • Slobodecki[icaron] , L.N. 1958 . S.L. Sobolev's spaces of fractional order and their application to boundary problems for partial differential equations . Dokl Akad. Nauk SSR , 118 : 243 – 246 . Russian
  • Sobolev , S.L. 1938 . On a theorem of functional analysis . Matem. Sbornik , 4 : 471 – 497 . Russian
  • Speck , F.-O. 1976 . “ Uber verallgemeinerte Faltungsoperatoren und ihre Symbole ” . In Function Theoretic Methods for Partial Differential Equations , Edited by: Meister , V.E. , Weck , N. and Wendland , W.L. 459 – 471 . Berlin : Springer .
  • Speck , F.-O. 1985 . General Wiener-Hopf Factorization Methods , London : Pitman .
  • Stein , E.M. 1970 . Singular Integrals and Differentiability Properties of Functions , Princeton : Princeton University Press .
  • Titchmarsh , E.G. 1937 . Introduction to the Theory of Fourier Integrals , Oxford : Clarendon Press .
  • Triebel , H. 1978 . Interpolation Theory, Function Spaces, Differential Operators , Amsterdam : North Holland .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.