Singular Integrals and Commutators in Generalized Morrey Spaces

By Lubomira G. Softova. 2002

79 citations recorded by the source corpus.

AbstractWe consider a singular an integral operator $${\fancyscript K}$$ with a variable Calderón–Zygmund type kernel k(x; ξ), x ∈ ℝn, ξ ∈ ℝn\{0}, satisfying a mixed homogeneity condition of the form $$ k{\left( {x;\mu ^{{\alpha _{1} }} \xi _{1} , \ldots ,\mu ^{{\alpha _{n} }} \xi _{n} } \right)} = \mu ^{{ - {\sum\nolimits_{i = 1}^n {\alpha _{i} } }}} k{\left( {x;\xi } \right)},\alpha _{i} \geqslant 1 $$ and μ > 0. The continuity of this operator in Lp(ℝn) is well studied by Fabes and Rivière. Our goal is to extend their result to generalized Morrey spaces Lp,ω(ℝn), p ∈ (1,∞) with a weight ω satisfying suitable dabbling and integral conditions. A special attention is paid to the commutator $${\fancyscript C}$$ [a, k] = $${\fancyscript K}$$a − a$${\fancyscript K}$$ with the operator of multiplication by BMO functions.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5e0f77ae91bd765f969bd7958b7fac37e475b914

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In Applied Mathematics

  1. Yoshihiro Sawano
  2. S. Samko
  3. Natasha Samko
  4. H. Rafeiro
  5. V. Kokilashvili
  6. Kwok-Pun Ho
  7. Dachun Yang
  8. Shohei Nakamura

In Mathematical Physics

  1. S. Samko
  2. Yoshihiro Sawano
  3. Natasha Samko
  4. H. Rafeiro
  5. Dachun Yang
  6. V. Kokilashvili
  7. Kwok-Pun Ho
  8. Wen Yuan

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