  We study variable range hopping in the quantum Hall effect regime in the
presence of a metallic gate parallel to the plane of a two-dimensional electron
gas. Screening of the Coulomb interaction by the gate causes the partial
``filling'' of the Coulomb gap in the density of localized states. At low
enough temperatures this leads to a substantial enhancement and a new
temperature behavior of the hopping conductivity. As a result, the diagonal
conductivity peaks become much wider. The power law dependence of the width of
the peaks on the temperature changes: the corresponding exponent turns out to
be twice as small as that for gateless structures. The width dependences on the
current in non-ohmic regime and on the frequency for the absorption of the
electromagnetic waves experience a similar modification. The experimental
observation of the crossovers predicted may demonstrate the important role of
the Coulomb interaction in the integer quantum Hall regime.
