Compactness of Toeplitz operators with continuous symbols on pseudoconvex domains in $\mathbb{C}^n$

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Abstract: Let

O m e g a

be a bounded pseudoconvex domain in

m a t h b b C^{n}

with Lipschitz boundary and

p h i

be a continuous function on

o v e r l i n e O m e g a

. We show that the Toeplitz operator

T_{p h i}

with symbol

p h i

is compact on the weighted Bergman space if and only if

p h i

vanishes on the boundary of

O m e g a

. We also show that compactness of the Toeplitz operator

T_{p h i}^{p, q}

on

o v e r l i n e p a r t i a l

-closed

(p, q)

-forms for

0 l e q p l e q n

and

q g e q 1

is equivalent to

p h i = 0

on

O m e g a

.

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