Dyadic fractional Sobolev spaces satisfy the expected embeddings and form an algebra under pointwise multiplication for sufficiently high regularity, with explicit counterexamples showing the algebra property fails at low regularity.
Two weight norm inequalities for fractional integral operators and commutators
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abstract
In these lecture notes we describe some recent work on two weight norm inequalities for fractional integral operators, also known as Riesz potentials, and for commutators of fractional integrals. These notes are based on three lectures delivered at the 6th International Course of Mathematical Analysis in Andalucia, held in Antequera, Spain, September 8-12, 2014. They are, however, greatly expanded to include both new results and many details that I did not present in my lectures due to time constraints.
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UNVERDICTED 4representative citing papers
The Adams trace inequality extends to product Morrey spaces via a Hedberg-type inequality.
Sufficient conditions are established for multilinear embedding theorems with fractional sparse operators on power weights and for L^p to L^q bounds on fractional Schrödinger operators.
The Kerman-Sawyer trace inequality extends to product Morrey spaces via parallel corona decomposition.
citing papers explorer
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Dyadic fractional Sobolev spaces: Embeddings and algebra property
Dyadic fractional Sobolev spaces satisfy the expected embeddings and form an algebra under pointwise multiplication for sufficiently high regularity, with explicit counterexamples showing the algebra property fails at low regularity.
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The Adams trace theorem for product Morrey spaces
The Adams trace inequality extends to product Morrey spaces via a Hedberg-type inequality.
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Multilinear embedding theorem for fractional sparse operators
Sufficient conditions are established for multilinear embedding theorems with fractional sparse operators on power weights and for L^p to L^q bounds on fractional Schrödinger operators.
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The Kerman-Sawyer trace theorem for product Morrey spaces
The Kerman-Sawyer trace inequality extends to product Morrey spaces via parallel corona decomposition.